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Author ID: rhoades.billy-e Recent zbMATH articles by "Rhoades, Billy E."
Published as: Rhoades, B. E.; Rhoades, Billy E.; Rhoades, B.
Homepage: http://www.math.indiana.edu/people/profile.phtml?id=rhoades
External Links: MGP
Documents Indexed: 411 Publications since 1959
1 Contribution as Editor
Reviewing Activity: 169 Reviews
Biographic References: 2 Publications
Co-Authors: 119 Co-Authors with 233 Joint Publications
2,850 Co-Co-Authors
all top 5

Co-Authors

169 single-authored
36 Savaş, Ekrem
20 Şoltuz, Ştefan M.
17 Abbas, Mujahid
14 Móricz, Ferenc
10 Park, Sehie
9 Mittal, Madan Lal
7 Hicks, Troy L.
6 Jungck, Gerald F.
6 Radenovic, Stojan
6 Vaezpour, Seyyed Mansour
5 Aydin Akgun, F.
4 Dhage, Bapurao C.
4 Khan, Safeer Hussain
4 Nuray, Fatih
4 Patterson, Richard F.
4 Rhaly, Henry Crawford jun.
4 Selmanogullari, T.
4 Sessa, Salvatore
3 Asadi, Mehdi
3 Chugh, Renu
3 Hussain, Nawab
3 Khan, Mohammed Saeed
3 Kuttner, Brian
3 Nazir, Talat
3 Qing, Yuan
3 Saadati, Reza
3 Sen, Pali
3 Şevli, Hamdullah
3 Turkoglu, Duran
3 Xue, Zhiqun
3 Yildirim, Mustafa
3 Zoto, Kastriot
2 Aggarwal, Madhu
2 Albayrak, Inci
2 Dolas, Uday
2 Esmaily, Jafar
2 Gürsoy, Faik
2 Jain, Mukesh Kumar
2 Kadian, Tamanna
2 Karakaya, Vatan
2 Lakzian, Hossein
2 Liu, Matthew
2 Lv, Guiwen
2 Mishra, Swami Nath
2 Mishra, Vishnu Narayan
2 Moon, Kwon Bai
2 Rakočević, Vladimir
2 Rathore, Mahendra Singh
2 Ray, Barada Kinkar
2 Saliga, Linda Marie
2 Shi, Xianliang
2 Singh, Kanhaya Lal
2 Singh, Mradul Veer
2 Singh, Shyam Lal
2 Singh, Uaday
2 Soleimani, Hossein
2 Watson, Bruce Brigham
2 Whitfield, John Howard Mervyn
2 Yıldırım, İsa
1 Akgün, Fatma Aydin
1 Altun, Ishak
1 Aydi, Hassen Mohamed
1 Bosede, Alfred Olufemi
1 Cass, Frank Peter
1 Chauhan, Manmohan Singh
1 Cho, Yeol Je
1 Choudhury, Binayak Samadder
1 Cvetković, Marija S.
1 DeFranza, James
1 Dikshit, Ganesh Datta
1 Dutta, Hemen
1 Fleming, Daniel J.
1 Garsia, Adriano M.
1 Gavala, G. W.
1 Górnicki, Jarosław
1 Haghi, Robab Hamlbarani
1 Haglund, James
1 Hu, Thakyin
1 Huang, Jui-Chi
1 Ibrahim, Rabha Waell
1 Jakimovski, Amnon
1 Janković, Slobodanka
1 Kadelburg, Zoran
1 Kalinde, Albert K.
1 Kang, Shin Min
1 Konar, Pulak
1 Kulshrestha, Chitra
1 Li, Jinlu
1 Long, Wei
1 Mayes, Vivienne
1 Metiya, Nikhilesh
1 Mohanraj, R.
1 Nashine, Hemant Kumar
1 Ozkoklu, Kevser
1 Pant, Rajendra Prasad
1 Pathan, A. M.
1 Powell, Robert E.
1 Rahimi, Hamidreza
1 Rajović, Miloje
1 Rani, Anju
...and 19 more Co-Authors
all top 5

Serials

27 Indian Journal of Pure & Applied Mathematics
27 International Journal of Mathematics and Mathematical Sciences
21 Fixed Point Theory and Applications
19 Journal of Mathematical Analysis and Applications
18 Applied Mathematics and Computation
12 Mathematica Japonica
11 Mathematics Seminar Notes
9 Jnanabha
9 Tamkang Journal of Mathematics
8 Pacific Journal of Mathematics
8 Journal of Advanced Mathematical Studies
7 Indian Journal of Mathematics
7 Mathematische Zeitschrift
6 Acta Scientiarum Mathematicarum
6 Transactions of the American Mathematical Society
6 Mathematical Communications
5 Integral Equations and Operator Theory
5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
5 Proceedings of the American Mathematical Society
5 Applied Mathematics Letters
5 Panamerican Mathematical Journal
5 Fixed Point Theory
5 Sarajevo Journal of Mathematics
4 Computers & Mathematics with Applications
4 Houston Journal of Mathematics
4 Bulletin of the Calcutta Mathematical Society
4 Canadian Mathematical Bulletin
4 Demonstratio Mathematica
4 Acta Mathematica Hungarica
4 Journal of Inequalities and Applications
3 Linear and Multilinear Algebra
3 Mathematical Proceedings of the Cambridge Philosophical Society
3 Rocky Mountain Journal of Mathematics
3 Commentationes Mathematicae Universitatis Carolinae
3 Mathematica Slovaca
3 Publicationes Mathematicae Debrecen
3 Soochow Journal of Mathematics
3 Analysis
3 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali
3 Filomat
3 Mathematical Inequalities & Applications
3 Analysis (München)
3 Journal of Computational Analysis and Applications
2 American Mathematical Monthly
2 Periodica Mathematica Hungarica
2 Commentarii Mathematici Universitatis Sancti Pauli
2 Publications de l’Institut Mathématique. Nouvelle Série
2 Ranchi University Mathematical Journal
2 Journal of National Academy of Mathematics, India
2 Radovi Matematički
2 Journal of the Australian Mathematical Society. Series A
2 Linear Algebra and its Applications
2 Revue d’Analyse Numérique et de Théorie de l’Approximation
2 Abstract and Applied Analysis
2 Taiwanese Journal of Mathematics
2 Nonlinear Functional Analysis and Applications
2 Hacettepe Journal of Mathematics and Statistics
2 Carpathian Journal of Mathematics
2 Proceedings of the Estonian Academy of Sciences
2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
1 Analysis Mathematica
1 Bulletin of the Australian Mathematical Society
1 Mathematics Magazine
1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica
1 Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie. Nouvelle Série
1 Fasciculi Mathematici
1 Fundamenta Mathematicae
1 Hokkaido Mathematical Journal
1 Illinois Journal of Mathematics
1 Journal of Approximation Theory
1 The Journal of the Indian Mathematical Society. New Series
1 Journal of the London Mathematical Society. Second Series
1 Kodai Mathematical Journal
1 Mathematische Nachrichten
1 Mathématica – Revue d’Analyse Numérique et de Théorie de l’Approximation. Mathématica
1 Mathematica Scandinavica
1 Monatshefte für Mathematik
1 Numerical Functional Analysis and Optimization
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Proceedings of the London Mathematical Society. Third Series
1 Real Analysis Exchange
1 Rendiconti del Circolo Matemàtico di Palermo. Serie II
1 Rendiconti del Seminario Matematico della Università di Padova
1 Revista de la Unión Matemática Argentina
1 Constructive Approximation
1 Mathematical and Computer Modelling
1 Journal of Natural & Physical Sciences
1 Alkalmazott Matematikai Lapok. A Magyar Tudomanyos Akademia. Matematikai es Fizikai Tudomanyok Osztalyanak Közlemenyei
1 Glasnik Matematički. Serija III
1 Stochastic Processes and their Applications
1 Studia Universitatis Babeș-Bolyai. Mathematica
1 Bulletin de l’Académie Polonaise des Sciences. Série des Sciences Mathématiques
1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
1 New Zealand Journal of Mathematics
1 Far East Journal of Mathematical Sciences
1 Communications on Applied Nonlinear Analysis
1 Mathematical Sciences Research Hot-Line
1 Annals of Combinatorics
1 International Journal of Mathematics, Game Theory and Algebra
1 Mathematica Moravica
...and 19 more Serials

Publications by Year

Citations contained in zbMATH Open

291 Publications have been cited 3,506 times in 2,284 Documents Cited by Year
Some theorems on weakly contractive maps. Zbl 1042.47521
Rhoades, B. E.
353
2001
A comparison of various definitions of contractive mappings. Zbl 0365.54023
Rhoades, B. E.
312
1977
Fixed points for set valued functions without continuity. Zbl 0904.54034
Jungck, G.; Rhoades, B. E.
177
1998
Comments on two fixed point iteration methods. Zbl 0353.47029
Rhoades, B. E.
122
1976
Almost convergence of double sequences and strong regularity of summability matrices. Zbl 0675.40004
Móricz, F.; Rhoades, B. E.
99
1988
Fixed and periodic point results in cone metric spaces. Zbl 1167.54014
Abbas, Mujahid; Rhoades, B. E.
96
2009
Fixed point theorems in generalized partially ordered G-metric spaces. Zbl 1202.54042
Saadati, R.; Vaezpour, S. M.; Vetro, P.; Rhoades, B. E.
88
2010
Fixed point iterations for certain nonlinear mappings. Zbl 0807.47045
Rhoades, B. E.
80
1994
Common fixed point results for noncommuting mappings without continuity in generalized metric spaces. Zbl 1185.54037
Abbas, M.; Rhoades, B. E.
79
2009
Two fixed-point theorems for mappings satisfying a general contractive condition of integral type. Zbl 1052.47052
Rhoades, B. E.
73
2003
Fixed point theorem for two non-self mappings in cone metric spaces. Zbl 1186.65073
Radenović, Stojan; Rhoades, B. E.
61
2009
Fixed point theorems for occasionally weakly compatible mappings. Zbl 1118.47045
Jungck, G.; Rhoades, B. E.
58
2006
A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type. Zbl 1113.54027
Vijayaraju, P.; Rhoades, B. E.; Mohanraj, R.
51
2005
Property P in G-metric spaces. Zbl 1203.54037
Chugh, Renu; Kadian, Tamanna; Rani, Anju; Rhoades, B. E.
51
2010
Fixed point iterations using infinite matrices. Zbl 0285.47038
Rhoades, B. E.
49
1974
Fixed point theorems for generalized weakly contractive mappings. Zbl 1218.54036
Choudhury, Binayak S.; Konar, P.; Rhoades, B. E.; Metiya, N.
47
2011
A Banach type fixed point theorem. Zbl 0432.47036
Hicks, T. L.; Rhoades, B. E.
44
1979
Statistical convergence of sequences of sets. Zbl 1287.40004
Nuray, Fatih; Rhoades, B. E.
44
2012
Fixed point theorems and stability results for fixed point iteration procedures. Zbl 0692.54027
Rhoades, B. E.
42
1990
Fixed points of weakly compatible maps satisfying a general contractive condition of integral type. Zbl 1153.54022
Altun, Ishak; Türkoğlu, Duran; Rhoades, Billy E.
40
2007
Fixed point theorems and stability results for fixed point iteration procedures. II. Zbl 0794.54048
Rhoades, B. E.
39
1993
Using infinite matrices to approximate functions of class Lip\((\alpha ,p)\) using trigonometric polynomials. Zbl 1106.42001
Mittal, M. L.; Rhoades, B. E.; Mishra, V. N.; Singh, Uaday
37
2007
Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type. Zbl 1348.54044
Cho, Yeol; Rhoades, Billy E.; Saadati, Reza; Samet, Bessem; Shatanawi, Wasfi
35
2012
Fixed point theory in symmetric spaces with applications to probabilistic spaces. Zbl 0947.54022
Hicks, Troy L.; Rhoades, B. E.
29
1999
The equivalence between Mann-Ishikawa iterations and multistep iteration. Zbl 1064.47070
Rhoades, B. E.; Soltuz, Stefan M.
29
2004
Contractive definitions and continuity. Zbl 0649.54024
Rhoades, B. E.
28
1988
A fixed point theorem for some non-self-mappings. Zbl 0396.47038
Rhoades, B. E.
26
1978
Assad-Kirk-type fixed point theorems for a pair of nonself mappings on cone metric spaces. Zbl 1186.54035
Janković, S.; Kadelburg, Z.; Radenović, S.; Rhoades, B. E.
25
2009
The fine spectra for weighted mean operators. Zbl 0501.40007
Rhoades, B. E.
25
1983
Some fixed point iteration procedures. Zbl 0716.47030
Rhoades, B. E.
24
1991
Common fixed points for four maps in cone metric spaces. Zbl 1197.54050
Abbas, Mujahid; Rhoades, B. E.; Nazir, Talat
23
2010
More maps for which \(F(T)=F(T^n)\). Zbl 1147.47041
Jeong, G. S.; Rhoades, B. E.
23
2007
Fixed points for \((\varphi,\psi,p)\)-weakly contractive mappings in metric spaces with image-distance. Zbl 06281853
Lakzian, Hossein; Aydi, Hassen; Rhoades, B. E.
21
2013
Data dependence results of new multi-step and S-iterative schemes for contractive-like operators. Zbl 1423.47041
Gürsoy, Faik; Karakaya, Vatan; Rhoades, Billy E.
21
2013
Spectra of some Hausdorff operators. Zbl 0223.47017
Rhoades, B. E.
20
1971
Meir-Keeler type contractive conditions. Zbl 0454.54030
Park, Sehie; Rhoades, B. E.
20
1981
\(T\)-stability of Picard iteration in metric spaces. Zbl 1145.54328
Qing, Yuan; Rhoades, B. E.
19
2008
Inclusion theorems for absolute matrix summability methods. Zbl 0936.40004
Rhoades, B. E.
17
1999
The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps. Zbl 1053.47055
Rhoades, B. E.; Şoltuz, Ştefan M.
17
2004
Approximation of signals of class \(Lip(\alpha , p)\) by linear operators. Zbl 1213.42006
Mittal, M. L.; Rhoades, B. E.; Sonker, Smita; Singh, U.
16
2011
Coincidence theorems for some multivalued mappings. Zbl 0571.54034
Rhoades, B. E.; Singh, S. L.; Kulshrestha, Chitra
15
1984
A general principle for Ishikawa iterations for multi-valued mappings. Zbl 0898.47046
Hu, Thakyin; Huang, Jui-Chi; Rhoades, B. E.
15
1997
On the degree of approximation of continuous functions by using linear operators on their Fourier series. Zbl 0958.42001
Mittal, M. L.; Rhoades, B. E.
14
1999
Some generalizations for \((\alpha - \psi,\phi)\)-contractions in \(b\)-metric-like spaces and an application. Zbl 1462.54108
Zoto, Kastriot; Rhoades, B. E.; Radenović, Stojan
14
2017
A fixed fuzzy point for fuzzy mapping in complete metric spaces. Zbl 1089.54518
Turkoglu, D.; Rhoades, B. E.
14
2005
Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings satisfying generalized contractive condition of integral type. Zbl 1153.54307
Abbas, Mujahid; Rhoades, B. E.
14
2007
Operators of A - p type. Zbl 0357.47020
Rhoades, B. E.
14
1976
On the degree of approximation of functions belonging to a Lipschitz class by Hausdorff means of its Fourier series. Zbl 1213.42007
Rhoades, B. E.; Ozkoklu, Kevser; Albayrak, Inci
14
2011
Common fixed point theorems for occasionally weakly compatible mappings satisfying a generalized contractive condition. Zbl 1175.47050
Abbas, Mujahid; Rhoades, B. E.
13
2008
Coincidence point theorem for generalized weakly contractions in ordered metric spaces. Zbl 06313468
Esmaily, Jafar; Vaezpour, S. Mansour; Rhoades, B. E.
13
2012
Stability of Picard and Mann iteration for a general class of functions. Zbl 1210.47093
Bosede, Alfred Olufemi; Rhoades, B. E.
13
2010
Degree of approximation to functions in a normed space. Zbl 0945.42001
Mittal, M. L.; Rhoades, B. E.
12
2000
Combinatorics of Tesler matrices in the theory of parking functions and diagonal harmonics. Zbl 1291.05203
Armstrong, D.; Garsia, A.; Haglund, J.; Rhoades, B.; Sagan, B.
12
2012
On generalizations of the Meir-Keeler type contraction maps. Zbl 0711.54028
Rhoades, B. E.; Park, Sehie; Moon, Kwon Bai
12
1990
Contraction type mappings on a 2-metric space. Zbl 0424.54038
Rhoades, B. E.
12
1979
Fixed point theorems for two new classes of multivalued mappings. Zbl 1173.47311
Abbas, Mujahid; Rhoades, B. E.
12
2009
The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically pseudocontractive map. Zbl 1045.47057
Rhoades, B. E.; Şoltuz, Ştefan M.
12
2003
Comments on the rate of convergence between Mann and Ishikawa iterations applied to Zamfirescu operators. Zbl 1203.47076
Qing, Yuan; Rhoades, B. E.
12
2008
A one-step iterative process for two multivalued nonexpansive mappings in Banach spaces. Zbl 1223.47081
Khan, Safeer Hussain; Yildirim, Isa; Rhoades, B. E.
12
2011
Current topics in summability theory and applications. Zbl 1348.40001
12
2016
Contractive definitions revisited. Zbl 0528.54037
Rhoades, B. E.
11
1983
On the equivalence of Mann and Ishikawa iteration methods. Zbl 1014.47052
Rhoades, B. E.; Soltuz, Stefan M.
11
2003
A fixed point theorem for non-self set-valued mappings. Zbl 0882.47038
Rhoades, B. E.
11
1997
Some notes on the paper “The equivalence of cone metric spaces and metric spaces”. Zbl 1273.54040
Asadi, Mehdi; Rhoades, Billy E.; Soleimani, Hossein
10
2012
Spectra and fine spectra for factorable matrices. Zbl 1097.47032
Rhoades, B. E.; Yildirim, M.
10
2005
Maps satisfying generalized contractive conditions of integral type for which \(F(T)=F(T^n)\). Zbl 1161.54024
Rhoades, B. E.; Abbas, M.
10
2008
Hausdorff matrices as bounded operators over \(l^p\). Zbl 0273.47012
Jakimovski, Amnon; Rhoades, Billy E.; Tzimbalario, Jean
10
1974
Some fixed point theorems for compatible maps. Zbl 0783.54038
Jungck, G.; Rhoades, B. E.
10
1993
Fixed points and continuity for multivalued mappings. Zbl 0746.54017
Hicks, Troy; Rhoades, B. E.
9
1992
Approximation of functions in the generalized Zygmund class using Hausdorff means. Zbl 1360.42005
Singh, Mradul Veer; Mittal, M. L.; Rhoades, B. E.
9
2017
Corrections to: On generalizations of the Meir-Keeler type contraction maps. Zbl 0790.54055
Jungck, Gerald; Moon, Kwon Bai; Park, Sehie; Rhoades, B. E.
9
1993
Necessary and sufficient Tauberian conditions for certain weighted mean methods of summability. Zbl 0833.40004
Móricz, F.; Rhoades, B. E.
9
1995
Fixed and periodic point theorems for \(T\)-contractions on cone metric spaces. Zbl 1324.54085
Rahimi, Hamidreza; Rhoades, B. E.; Radenović, Stojan; Rad, Ghasem Soleimani
8
2013
The degree of approximation of functions, and their conjugates, belonging to several general Lipschitz classes by Hausdorff matrix means of the Fourier series and conjugate series of a Fourier series. Zbl 1322.42008
Rhoades, B. E.
8
2014
The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators. Zbl 1045.47058
Rhoades, B. E.; Şoltuz, Ştefan M.
8
2003
Hausdorff summability methods. Zbl 0136.35305
Rhoades, B. E.
8
1961
The equivalence between the \(T\)-stabilities of Mann and Ishikawa iterations. Zbl 1095.47044
Rhoades, B. E.; Şoltuz, Ştefan M.
8
2006
Spectra for factorable matrices on \(\ell^p\). Zbl 1093.40004
Rhoades, B. E.; Yildirim, M.
8
2006
The fine spectra for weighted mean operators in \(B(\ell ^ p)\). Zbl 0681.47012
Rhoades, B. E.
8
1989
On \(T\)-stability of Picard iteration in cone metric spaces. Zbl 1202.54030
Asadi, M.; Soleimani, H.; Vaezpour, S. M.; Rhoades, B. E.
8
2009
On some new sequence spaces of invariant means defined by Orlicz functions. Zbl 1010.46006
Savas, E.; Rhoades, B. E.
8
2002
Approximation of signals (functions) belonging to the weighted \(W(L_{p},\xi (t))\)-class by linear operators. Zbl 1126.42001
Mittal, M. L.; Rhoades, B. E.; Mishra, Vishnu Narayan
8
2006
A fixed point theorem for a multivalued non-self mapping. Zbl 0849.47032
Rhoades, B. E.
8
1996
Lower bounds for some matrices. II. Zbl 0697.15009
Rhoades, B. E.
8
1990
Some results about T-stability and almost T-stability. Zbl 1281.47052
Rezapour, Sh.; Haghi, R. H.; Rhoades, B. E.
8
2011
Coupled coincidence points for two mappings in metric spaces and cone metric spaces. Zbl 1414.54021
Long, Wei; Rhoades, Billy E.; Rajović, Miloje
7
2012
Finding common fixed points of nonexpansive mappings by iteration. Zbl 0965.47035
Rhoades, B. E.
7
2000
On the degree of approximation of functions belonging to the weighted \((L^p,\xi(t))\) class by Hausdorff means. Zbl 0999.42005
Rhoades, B. E.
7
2001
Double absolute summability factor theorems and applications. Zbl 1167.40302
Savaş, Ekrem; Rhoades, B. E.
7
2008
Triangular summability methods and the boundary of the maximal group. Zbl 0179.08801
Rhoades, B. E.
7
1968
A general fixed point theorem for involutions. Zbl 0847.47038
Górnicki, J.; Rhoades, B. E.
7
1996
Fixed point iterations using infinite matrices. II. Zbl 0303.47036
Rhoades, B. E.
7
1974
Some classes of doubly infinite matrices. Zbl 0755.40009
Rhoades, B. E.
6
1992
Fixed points for pairs of mappings in d-complete topological spaces. Zbl 0796.54049
Hicks, Troy L.; Rhoades, B. E.
6
1993
Approximation by matrix means of double Fourier series to continuous functions in two variables. Zbl 0953.42007
Mittal, M. L.; Rhoades, B. E.
6
1999
Some fixed point theorems using weaker Meir-Keeler function in metric spaces with \(w\)-distance. Zbl 1428.47019
Lakzian, Hossein; Rhoades, B. E.
6
2019
An equivalent reformulation of summability by weighted mean methods, revisited. Zbl 1052.40009
Móricz, Ferenc; Rhoades, Billy E.
6
2002
Convergence theorems for \(I\)-nonexpansive mapping. Zbl 1146.47045
Rhoades, B. E.; Temir, Seyit
6
2006
Relations between \((N,p_ n)\) and \((\overline N,p_ n)\) summability. Zbl 0164.06702
Kuttner, Brian; Rhoades, B. E.
6
1968
Properties of some \(q\)-Hausdorff matrices. Zbl 1291.15091
Aydin Akgun, F.; Rhoades, B. E.
6
2013
Unified Feng-Liu type fixed point theorems solving control problems. Zbl 07273574
Nashine, Hemant Kumar; Ibrahim, Rabha W.; Rhoades, B. E.; Pant, Rajendra
4
2021
Higher Specht bases for generalizations of the coinvariant ring. Zbl 1472.05151
Gillespie, M.; Rhoades, B.
1
2021
Some fixed point theorems using weaker Meir-Keeler function in metric spaces with \(w\)-distance. Zbl 1428.47019
Lakzian, Hossein; Rhoades, B. E.
6
2019
Common fixed point theorems for a class of \((s,q)\)-contractive mappings in \(b\)-metric-like spaces and applications to integral equations. Zbl 1496.54074
Zoto, Kastriot; Rhoades, Billy E.; Radenović, Stojan
5
2019
Correction to: “Some generalizations for \((\alpha-\psi,\phi)\)-contractions in \(b\)-metric-like spaces and an application”. Zbl 1462.54109
Zoto, Kastriot; Rhoades, B. E.; Radenović, Stojan
2
2018
Some generalizations for \((\alpha - \psi,\phi)\)-contractions in \(b\)-metric-like spaces and an application. Zbl 1462.54108
Zoto, Kastriot; Rhoades, B. E.; Radenović, Stojan
14
2017
Approximation of functions in the generalized Zygmund class using Hausdorff means. Zbl 1360.42005
Singh, Mradul Veer; Mittal, M. L.; Rhoades, B. E.
9
2017
General fixed point results in dislocated metric spaces. Zbl 1395.54047
Jungck, Gerald F.; Rhoades, B. E.
1
2017
Current topics in summability theory and applications. Zbl 1348.40001
12
2016
Some fixed point theorems in \(G\)-metric spaces which are special cases of metric space results. Zbl 06678594
Rhoades, B. E.
1
2016
Fixed point theorems for contractive mappings of Perov type. Zbl 1354.47036
Cvetković, Marija; Rakočević, Vladimir; Rhoades, B. E.
2
2015
The degree of approximation of functions, and their conjugates, belonging to several general Lipschitz classes by Hausdorff matrix means of the Fourier series and conjugate series of a Fourier series. Zbl 1322.42008
Rhoades, B. E.
8
2014
Some convergence and stability results for the Kirk multistep and Kirk-SP fixed point iterative algorithms. Zbl 1473.47035
Gürsoy, Faik; Karakaya, Vatan; Rhoades, B. E.
4
2014
Coupled fixed point theorems for generalized symmetric contractions in partially ordered metric spaces and applications. Zbl 1291.54059
Jain, M.; Tas, K.; Rhoades, B. E.; Gupta, N.
4
2014
The weighted mean operator on \(\ell^2\) with the weight sequence \(w_{ n} = n + 1\) is hyponormal. Zbl 1321.47079
Rhaly, H. C. jun.; Rhoades, B. E.
1
2014
Fixed points for \((\varphi,\psi,p)\)-weakly contractive mappings in metric spaces with image-distance. Zbl 06281853
Lakzian, Hossein; Aydi, Hassen; Rhoades, B. E.
21
2013
Data dependence results of new multi-step and S-iterative schemes for contractive-like operators. Zbl 1423.47041
Gürsoy, Faik; Karakaya, Vatan; Rhoades, Billy E.
21
2013
Fixed and periodic point theorems for \(T\)-contractions on cone metric spaces. Zbl 1324.54085
Rahimi, Hamidreza; Rhoades, B. E.; Radenović, Stojan; Rad, Ghasem Soleimani
8
2013
Properties of some \(q\)-Hausdorff matrices. Zbl 1291.15091
Aydin Akgun, F.; Rhoades, B. E.
6
2013
Coincidence and common fixed point theorems for a sequence of mappings in ordered metric spaces. Zbl 1298.54027
Esmaily, Jafar; Vaezpour, S. Mansour; Rhoades, B. E.
4
2013
Asymptotically and statistically equivalent functions defined on amenable semigroups. Zbl 1292.40002
Nuray, Fatih; Rhoades, B. E.
2
2013
Fixed points of multivalued mapping satisfying Ciric type contractive conditions in G-metric spaces. Zbl 1301.54057
Abbas, Mujahid; Nazır, Talat; Rhoades, B. E.
1
2013
Coupled fixed points of Geraghty-type mappings in \(G\)-metric spaces. Zbl 1278.54028
Chugh, Renu; Rhoades, B. E.; Aggarwal, Madhu
1
2013
Statistical convergence of sequences of sets. Zbl 1287.40004
Nuray, Fatih; Rhoades, B. E.
44
2012
Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type. Zbl 1348.54044
Cho, Yeol; Rhoades, Billy E.; Saadati, Reza; Samet, Bessem; Shatanawi, Wasfi
35
2012
Coincidence point theorem for generalized weakly contractions in ordered metric spaces. Zbl 06313468
Esmaily, Jafar; Vaezpour, S. Mansour; Rhoades, B. E.
13
2012
Combinatorics of Tesler matrices in the theory of parking functions and diagonal harmonics. Zbl 1291.05203
Armstrong, D.; Garsia, A.; Haglund, J.; Rhoades, B.; Sagan, B.
12
2012
Some notes on the paper “The equivalence of cone metric spaces and metric spaces”. Zbl 1273.54040
Asadi, Mehdi; Rhoades, Billy E.; Soleimani, Hossein
10
2012
Coupled coincidence points for two mappings in metric spaces and cone metric spaces. Zbl 1414.54021
Long, Wei; Rhoades, Billy E.; Rajović, Miloje
7
2012
Fixed point theorems for occasionally weakly compatible expansive mappings. Zbl 1270.47043
Jain, Mukesh Kumar; Rhoades, B. E.; Saluja, A. S.
2
2012
Some weakly contractive mapping theorems in partially ordered spaces and applications. Zbl 1274.54142
Rhoades, B. E.; Pathak, H. K.; Mishra, S. N.
2
2012
Almost statistical convergence in amenable semigroups. Zbl 1381.43005
Nuray, Fatih; Rhoades, B. E.
2
2012
The equivalence of generalized Hölder and Cesàro matrices. Zbl 1245.15032
Aydin Akgun, F.; Rhoades, B. E.
1
2012
The convergence theorems of Ishikawa iterative process with errors for \({\phi}\)-hemi-contractive mappings in uniformly smooth Banach spaces. Zbl 1398.47004
Xue, Zhiqun; Lv, Guiwen; Rhoades, B. E.
1
2012
A fixed point theorem of integral type. Zbl 1269.54030
Rhoades, B. E.
1
2012
Fixed point theorems for generalized weakly contractive mappings. Zbl 1218.54036
Choudhury, Binayak S.; Konar, P.; Rhoades, B. E.; Metiya, N.
47
2011
Approximation of signals of class \(Lip(\alpha , p)\) by linear operators. Zbl 1213.42006
Mittal, M. L.; Rhoades, B. E.; Sonker, Smita; Singh, U.
16
2011
On the degree of approximation of functions belonging to a Lipschitz class by Hausdorff means of its Fourier series. Zbl 1213.42007
Rhoades, B. E.; Ozkoklu, Kevser; Albayrak, Inci
14
2011
A one-step iterative process for two multivalued nonexpansive mappings in Banach spaces. Zbl 1223.47081
Khan, Safeer Hussain; Yildirim, Isa; Rhoades, B. E.
12
2011
Some results about T-stability and almost T-stability. Zbl 1281.47052
Rezapour, Sh.; Haghi, R. H.; Rhoades, B. E.
8
2011
On \(q\)-Hausdorff matrices. Zbl 1268.40005
Selmanogullari, T.; Savaş, E.; Rhoades, B. E.
5
2011
Coincidence point theorems for multivalued \(f\)-weak contraction mappings and applications. Zbl 1296.54048
Abbas, Mujahid; Hussain, Nawab; Rhoades, Billy E.
4
2011
Fixed point theorems for contractive mapping in cone metric spaces. Zbl 1217.54038
Asadi, Mehdi; Vaezpour, S. Mansour; Rakočević, Vladimir; Rhoades, Billy E.
3
2011
The spectra and fine spectra of factorable matrices on \(c_0\). Zbl 1232.40005
Rhoades, Billy E.; Yildirim, Mustafa
3
2011
Some kinds of convergence defined by Folner sequences. Zbl 1244.40003
Nuray, Fatih; Rhoades, Billy E.
3
2011
Necessary conditions for inclusion relations for double absolute summability. Zbl 1241.40003
Savaş, Ekrem; Rhoades, B. E.
1
2011
Size of convergence domains for generalized Hausdorff prime matrices. Zbl 1243.15018
Selmanogullari, T.; Savaş, E.; Rhoades, B. E.
1
2011
Erratum to: “A one-step iterative process for two multivalued nonexpansive mappings in Banach spaces”. Zbl 1236.47072
Khan, Safeer Hussain; Yildirim, Isa; Rhoades, B. E.
1
2011
Fixed point theorems in generalized partially ordered G-metric spaces. Zbl 1202.54042
Saadati, R.; Vaezpour, S. M.; Vetro, P.; Rhoades, B. E.
88
2010
Property P in G-metric spaces. Zbl 1203.54037
Chugh, Renu; Kadian, Tamanna; Rani, Anju; Rhoades, B. E.
51
2010
Common fixed points for four maps in cone metric spaces. Zbl 1197.54050
Abbas, Mujahid; Rhoades, B. E.; Nazir, Talat
23
2010
Stability of Picard and Mann iteration for a general class of functions. Zbl 1210.47093
Bosede, Alfred Olufemi; Rhoades, B. E.
13
2010
Comparison of the rate of convergence among Picard, Mann, Ishikawa, and Noor iterations applied to quasicontractive maps. Zbl 1206.47083
Rhoades, B. E.; Xue, Zhiqun
6
2010
A new one-step iterative scheme for approximating common fixed points of two multivalued nonexpansive mappings. Zbl 1226.47077
Khan, Safeer Hussain; Abbas, Mujahid; Rhoades, Billy E.
5
2010
Factorable generalized Hausdorff matrices. Zbl 1204.40005
Akgun, F. Aydin; Rhoades, B. E.
1
2010
Fixed and periodic point results in cone metric spaces. Zbl 1167.54014
Abbas, Mujahid; Rhoades, B. E.
96
2009
Common fixed point results for noncommuting mappings without continuity in generalized metric spaces. Zbl 1185.54037
Abbas, M.; Rhoades, B. E.
79
2009
Fixed point theorem for two non-self mappings in cone metric spaces. Zbl 1186.65073
Radenović, Stojan; Rhoades, B. E.
61
2009
Assad-Kirk-type fixed point theorems for a pair of nonself mappings on cone metric spaces. Zbl 1186.54035
Janković, S.; Kadelburg, Z.; Radenović, S.; Rhoades, B. E.
25
2009
Fixed point theorems for two new classes of multivalued mappings. Zbl 1173.47311
Abbas, Mujahid; Rhoades, B. E.
12
2009
On \(T\)-stability of Picard iteration in cone metric spaces. Zbl 1202.54030
Asadi, M.; Soleimani, H.; Vaezpour, S. M.; Rhoades, B. E.
8
2009
An inclusion theorem for double Cesàro matrices over the space of absolutely \(k\)-convergent double series. Zbl 1173.40302
Savaş, Ekrem; Rhoades, B. E.
3
2009
A fixed point result for asymptotically nonexpansive mappings on an unbounded set. Zbl 1249.47044
Abbas, M.; Rhoades, B. E.
3
2009
Every conservative double Hausdorff matrix is a \(k\)th absolutely summable operator. Zbl 1212.40011
Savaş, Ekrem; Rhoades, B. E.
2
2009
Four-dimensional matrix transformation and the double Gibbs’ phenomenon. Zbl 1181.40004
Patterson, Richard F.; Rhoades, Billy E.
1
2009
The point spectra of generalized Hausdorff matrices. Zbl 1193.47035
Rhoades, B. E.
1
2009
T-stability approach to variational iteration method for solving integral equations. Zbl 1175.54061
Saadati, R.; Vaezpour, S. M.; Rhoades, B. E.
1
2009
Common fixed points of generalized contractive multivalued mappings in cone metric spaces. Zbl 1201.54028
Abbas, Mujahid; Rhoades, B. E.; Nazir, Talat
1
2009
Necessary and sufficient condition for common fixed point theorems. Zbl 1181.54051
Rhoades, B. E.; Abbas, Mujahid
1
2009
\(T\)-stability of Picard iteration in metric spaces. Zbl 1145.54328
Qing, Yuan; Rhoades, B. E.
19
2008
Common fixed point theorems for occasionally weakly compatible mappings satisfying a generalized contractive condition. Zbl 1175.47050
Abbas, Mujahid; Rhoades, B. E.
13
2008
Comments on the rate of convergence between Mann and Ishikawa iterations applied to Zamfirescu operators. Zbl 1203.47076
Qing, Yuan; Rhoades, B. E.
12
2008
Maps satisfying generalized contractive conditions of integral type for which \(F(T)=F(T^n)\). Zbl 1161.54024
Rhoades, B. E.; Abbas, M.
10
2008
Double absolute summability factor theorems and applications. Zbl 1167.40302
Savaş, Ekrem; Rhoades, B. E.
7
2008
Simpler is also better in approximating fixed points. Zbl 1170.65034
Abbas, M.; Khan, Safeer Hussain; Rhoades, B. E.
5
2008
Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings defined on symmetric space. Zbl 1152.54030
Abbas, Mujahid; Rhoades, B. E.
5
2008
Common fixed point, best approximation and generalized \(f\)-weak contraction multivalued mapping in \(p\)-normed spaces. Zbl 1158.47039
Abbas, M.; Rhoades, B. E.
3
2008
A general fixed point theorem for multi-valued mapping in uniform space. Zbl 1162.54020
Türkoğlu, D.; Rhoades, B. E.
2
2008
On the Cesáro summability of double series. Zbl 1148.40004
Savaş, E.; Şevli, H.; Rhoades, B. E.
2
2008
A fixed point theorem for certain operators. Zbl 1172.54029
Rhoades, B. E.
1
2008
Erratum: Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings satisfying generalized contractive condition of integral type revisited. Zbl 1156.54302
Abbas, M.; Rhoades, B. E.
1
2008
Fixed points of weakly compatible maps satisfying a general contractive condition of integral type. Zbl 1153.54022
Altun, Ishak; Türkoğlu, Duran; Rhoades, Billy E.
40
2007
Using infinite matrices to approximate functions of class Lip\((\alpha ,p)\) using trigonometric polynomials. Zbl 1106.42001
Mittal, M. L.; Rhoades, B. E.; Mishra, V. N.; Singh, Uaday
37
2007
More maps for which \(F(T)=F(T^n)\). Zbl 1147.47041
Jeong, G. S.; Rhoades, B. E.
23
2007
Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings satisfying generalized contractive condition of integral type. Zbl 1153.54307
Abbas, Mujahid; Rhoades, B. E.
14
2007
The question of equivalence for generalized Hausdorff matrices. Zbl 1112.15025
Albayrak, Inci; Rhoades, B. E.
4
2007
Double summability factor theorems and applications. Zbl 1114.40003
Savaş, Ekrem; Rhoades, B. E.
3
2007
Common fixed point and invariant approximation results for Gregus type \(I\)-contractions. Zbl 1140.47043
Hussain, N.; Rhoades, B. E.; Jungck, G.
3
2007
A note on \(|A|_{k}\) summability factors. Zbl 1115.40004
Savaş, E.; Rhoades, B. E.
1
2007
A biased discussion of fixed point theory. Zbl 1174.54385
Rhoades, B. E.
1
2007
Common fixed point theorems for asymptotically \(I\)-contractive mappings without convexity. Zbl 1145.47043
Pathak, H. K.; Rhoades, B. E.; Khan, M. S.
1
2007
Fixed point theorems for occasionally weakly compatible mappings. Zbl 1118.47045
Jungck, G.; Rhoades, B. E.
58
2006
The equivalence between the \(T\)-stabilities of Mann and Ishikawa iterations. Zbl 1095.47044
Rhoades, B. E.; Şoltuz, Ştefan M.
8
2006
Spectra for factorable matrices on \(\ell^p\). Zbl 1093.40004
Rhoades, B. E.; Yildirim, M.
8
2006
Approximation of signals (functions) belonging to the weighted \(W(L_{p},\xi (t))\)-class by linear operators. Zbl 1126.42001
Mittal, M. L.; Rhoades, B. E.; Mishra, Vishnu Narayan
8
2006
Convergence theorems for \(I\)-nonexpansive mapping. Zbl 1146.47045
Rhoades, B. E.; Temir, Seyit
6
2006
\(C_{q}\)-commuting maps and invariant approximations. Zbl 1131.54027
Hussain, N.; Rhoades, B. E.
5
2006
A summability factor theorem for generalized absolute summability. Zbl 1116.40004
Rhoades, B. E.; Savaş, Ekrem
4
2006
On \(| A| _k\) summability factors. Zbl 1121.40009
Rhoades, B. E.; Savaş, E.
4
2006
Some sequence spaces which include \(c_0\) and \(c\). Zbl 1132.46005
Rhoades, B. E.
4
2006
...and 191 more Documents
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Cited by 1,833 Authors

87 Radenovic, Stojan
85 Rhoades, Billy E.
73 Abbas, Mujahid
68 Karapınar, Erdal
43 Imdad, Mohammad
41 Kadelburg, Zoran
40 Cho, Yeol Je
39 Kumam, Poom
39 Rakočević, Vladimir
38 Aydi, Hassen Mohamed
38 Hussain, Nawab
36 Savaş, Ekrem
34 Kang, Shin Min
33 Nashine, Hemant Kumar
32 Shatanawi, Wasfi A.
31 Sintunavarat, Wutiphol
27 Ćirić, Ljubomir B.
26 Chidume, Charles Ejike
26 Choudhury, Binayak Samadder
26 Shahzad, Naseer
25 Liu, Zeqing
25 Vetro, Calogero
24 Samet, Bessem
23 Nazir, Talat
21 Pant, Rajendra Prasad
21 Ume, Jeong Sheok
20 Azam, Akbar
20 Bisht, Ravindra Kishor
20 Mursaleen, Mohammad
20 Parvaneh, Vahid
20 Sarwar, Muhammad
20 Subramanian, Nagarajan
17 Chauhan, Sunny
17 Gu, Feng
17 Mishra, Vishnu Narayan
17 Zegeye, Habtu
16 Mishra, Lakshmi Narayan
15 Ansari, Arslan Hojat
15 Beg, Ismat
15 Chandok, Sumit
15 de la Sen, Manuel
15 Karakaya, Vatan
15 Mitrović, Zoran D.
15 Okeke, Godwin Amechi
15 Suantai, Suthep
14 Agarwal, Ravi P.
13 Altun, Ishak
13 Chang, Shih-Sen
13 Khan, Abdul Rahim
13 Mishra, Swami Nath
13 Petruşel, Adrian
13 Rafiq, Arif
13 Singh, Shyam Lal
13 Singh, Uaday
13 Zhu, Chuanxi
12 Abdeljawad, Thabet
12 Bakery, Awad A.
12 Saadati, Reza
12 Ulusu, Uǧur
12 Zhou, Haiyun
11 Akewe, Hudson
11 Ali, Javid
11 Başar, Feyzi
11 Çanak, İbrahim
11 Gopal, Dhananjay
11 Khan, Safeer Hussain
11 Kim, Jong Kyu
11 Mustafa, Zead
11 Nuray, Fatih
11 Paikray, Susanta Kumar
11 Razani, Abdolrahman
11 Sahu, Daya Ram
11 Soleimani Rad, Ghasem
11 Vetro, Francesca
10 Babu, Gutti Venkata Ravindranadh
10 Berinde, Vasile
10 Chugh, Renu
10 Esi, Ayhan
10 Gürsoy, Faik
10 Hazarika, Bipan
10 Kamran, Tayyab
10 Kumar, Sanjay V.
10 Kutbi, Marwan Amin
10 Mittal, Madan Lal
10 Pathak, Hemant Kumar
10 Postolache, Mihai
10 Sedghi, Shaban
10 Turinici, Mihai
9 Alotaibi, Abdullah M.
9 Damjanović, Boško
9 Dündar, Erdinç
9 Dutta, Hemen
9 Fadail, Zaid Mohammed
9 Gupta, Vishal
9 Metiya, Nikhilesh
9 Mohiuddine, Syed Abdul
9 Roldán-López-de-Hierro, Antonio-Francisco
9 Su, Yongfu
9 Tripathy, Binod Chandra
9 Vaezpour, Seyyed Mansour
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Cited in 261 Serials

269 Fixed Point Theory and Applications
110 Journal of Mathematical Analysis and Applications
94 Abstract and Applied Analysis
83 Journal of Inequalities and Applications
80 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
62 Applied Mathematics and Computation
59 Computers & Mathematics with Applications
52 Journal of Function Spaces
48 Applied Mathematics Letters
46 Filomat
43 Journal of Fixed Point Theory and Applications
36 International Journal of Mathematics and Mathematical Sciences
36 Mathematical and Computer Modelling
32 Demonstratio Mathematica
32 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
30 Thai Journal of Mathematics
29 Afrika Matematika
23 Boletim da Sociedade Paranaense de Matemática. Terceira Série
22 The Journal of Analysis
22 Journal of Applied Mathematics
22 Advances in Difference Equations
22 Journal of Nonlinear Science and Applications
21 Journal of Mathematics
19 Numerical Functional Analysis and Optimization
18 Rendiconti del Circolo Matemàtico di Palermo. Serie II
18 Nonlinear Functional Analysis and Applications
17 Chaos, Solitons and Fractals
17 Journal of the Egyptian Mathematical Society
16 Proceedings of the American Mathematical Society
15 Asian-European Journal of Mathematics
15 Nonlinear Analysis. Theory, Methods & Applications
14 Applied General Topology
14 Journal of Linear and Topological Algebra
13 Mathematische Zeitschrift
13 AIMS Mathematics
12 Journal of Computational and Applied Mathematics
12 Vietnam Journal of Mathematics
12 Mathematical Sciences
11 Ukrainian Mathematical Journal
11 Results in Mathematics
11 Acta Mathematica Sinica. English Series
11 South East Asian Journal of Mathematics and Mathematical Sciences
11 International Journal of Analysis
10 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
10 Acta Mathematica Hungarica
10 Mediterranean Journal of Mathematics
10 JP Journal of Fixed Point Theory and Applications
10 Palestine Journal of Mathematics
10 Electronic Journal of Mathematical Analysis and Applications EJMAA
10 Sahand Communications in Mathematical Analysis
10 Open Mathematics
9 Linear and Multilinear Algebra
9 Fasciculi Mathematici
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9 Applied Mathematics and Mechanics. (English Edition)
9 Positivity
9 Discrete Dynamics in Nature and Society
9 Nonlinear Analysis. Modelling and Control
9 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
8 Fuzzy Sets and Systems
8 Turkish Journal of Mathematics
8 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche
8 Journal of Nonlinear Analysis and Optimization: Theory & Applications
8 Journal of Classical Analysis
8 Asia Pacific Journal of Mathematics
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7 Arab Journal of Mathematical Sciences
7 Applied Mathematics E-Notes
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7 Fixed Point Theory
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7 ISRN Mathematical Analysis
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6 Analysis Mathematica
6 Bulletin of the Australian Mathematical Society
6 Archiv der Mathematik
6 Communications of the Korean Mathematical Society
6 Proyecciones
6 Arabian Journal of Mathematics
6 Mathematics
6 Topological Algebra and its Applications
6 Transactions of A. Razmadze Mathematical Institute
5 Mathematical Notes
5 Integral Equations and Operator Theory
5 Transactions of the American Mathematical Society
5 Topology and its Applications
5 Facta Universitatis. Series Mathematics and Informatics
5 Numerical Algorithms
5 Soft Computing
5 Novi Sad Journal of Mathematics
5 Communications de la Faculté des Sciences de l’Université d’Ankara. Séries A1. Mathematics and Statistics
5 Lobachevskii Journal of Mathematics
5 Journal of Function Spaces and Applications
5 European Journal of Pure and Applied Mathematics
5 Acta Universitatis Sapientiae. Mathematica
5 Journal of Applied Mathematics & Informatics
5 Chinese Journal of Mathematics
4 Applicable Analysis
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Cited in 49 Fields

1,246 General topology (54-XX)
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126 Numerical analysis (65-XX)
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87 Harmonic analysis on Euclidean spaces (42-XX)
57 Integral equations (45-XX)
44 Ordinary differential equations (34-XX)
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34 Calculus of variations and optimal control; optimization (49-XX)
27 Operations research, mathematical programming (90-XX)
25 Linear and multilinear algebra; matrix theory (15-XX)
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