Antony Vijesh, Villavarayan; Sumithra Rudresha, Shreyas; Abdulla, Mohammed Shahid A note on generalized second-order value iteration in Markov decision processes. (English) Zbl 07785183 J. Optim. Theory Appl. 199, No. 3, 1022-1049 (2023). MSC: 90Cxx 49-XX PDFBibTeX XMLCite \textit{V. Antony Vijesh} et al., J. Optim. Theory Appl. 199, No. 3, 1022--1049 (2023; Zbl 07785183) Full Text: DOI
Singh, Manoj K.; Singh, B. R.; Mishra, Deepak Kumar On the convergence of Newton-like MS method with dynamics and applications. (English) Zbl 07778315 S\(\vec{\text{e}}\)MA J. 80, No. 4, 663-686 (2023). MSC: 47H10 49M15 65K10 PDFBibTeX XMLCite \textit{M. K. Singh} et al., S\(\vec{\text{e}}\)MA J. 80, No. 4, 663--686 (2023; Zbl 07778315) Full Text: DOI
Regmi, Samundra; Argyros, Ioannis K.; George, Santhosh; Argyros, Michael Extended Kantorovich theory for solving nonlinear equations with applications. (English) Zbl 1506.65071 Comput. Appl. Math. 42, No. 2, Paper No. 76, 14 p. (2023). MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{S. Regmi} et al., Comput. Appl. Math. 42, No. 2, Paper No. 76, 14 p. (2023; Zbl 1506.65071) Full Text: DOI
Panayotaros, Panayotis; Vargas-Magaña, Rosa Maria Water wave problem with inclined walls. (English) Zbl 1502.76018 Eur. J. Mech., B, Fluids 96, 108-121 (2022). Reviewer: Vincent Duchêne (Rennes) MSC: 76B15 76B07 PDFBibTeX XMLCite \textit{P. Panayotaros} and \textit{R. M. Vargas-Magaña}, Eur. J. Mech., B, Fluids 96, 108--121 (2022; Zbl 1502.76018) Full Text: DOI arXiv
Xiao, Yao; Wu, Qingbiao; Zhang, Yuanyuan Newton-PGSS and its improvement method for solving nonlinear systems with saddle point Jacobian matrices. (English) Zbl 1477.65064 J. Math. 2021, Article ID 6636943, 18 p. (2021). MSC: 65F10 PDFBibTeX XMLCite \textit{Y. Xiao} et al., J. Math. 2021, Article ID 6636943, 18 p. (2021; Zbl 1477.65064) Full Text: DOI
Argyros, Ioannis K.; George, Santhosh; Sahu, Daya Ram Extensions of Kantorovich-type theorems for Newton’s method. (English) Zbl 1468.65062 Appl. Math. 47, No. 1, 145-153 (2020). MSC: 65J15 49M15 PDFBibTeX XMLCite \textit{I. K. Argyros} et al., Appl. Math. 47, No. 1, 145--153 (2020; Zbl 1468.65062) Full Text: DOI
Petruşel, A.; Rus, I. A. Graphic contraction principle and applications. (English) Zbl 07216131 Rassias, Themistocles M. (ed.) et al., Mathematical analysis and applications. Cham: Springer. Springer Optim. Appl. 154, 411-432 (2019). MSC: 47H10 54H25 47H09 34D10 45Gxx 45M10 PDFBibTeX XMLCite \textit{A. Petruşel} and \textit{I. A. Rus}, Springer Optim. Appl. 154, 411--432 (2019; Zbl 07216131) Full Text: DOI
Klatte, Diethard; Kummer, Bernd Nonsmooth Kantorovich-Newton methods: hypotheses and auxiliary problems. (English) Zbl 1427.49029 Vietnam J. Math. 47, No. 3, 639-657 (2019). MSC: 49M15 65J05 49J52 49M25 PDFBibTeX XMLCite \textit{D. Klatte} and \textit{B. Kummer}, Vietnam J. Math. 47, No. 3, 639--657 (2019; Zbl 1427.49029) Full Text: DOI
Ezquerro, J. A.; Hernández-Verón, M. A. Construction of simple majorizing sequences for iterative methods. (English) Zbl 1468.65064 Appl. Math. Lett. 98, 149-156 (2019). MSC: 65J15 PDFBibTeX XMLCite \textit{J. A. Ezquerro} and \textit{M. A. Hernández-Verón}, Appl. Math. Lett. 98, 149--156 (2019; Zbl 1468.65064) Full Text: DOI
Argyros, Ioannis K.; George, Santhosh Kantorovich-like convergence theorems for Newton’s method using restricted convergence domains. (English) Zbl 1482.49030 Numer. Funct. Anal. Optim. 40, No. 3, 303-318 (2019). MSC: 49M15 49J53 65G99 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. George}, Numer. Funct. Anal. Optim. 40, No. 3, 303--318 (2019; Zbl 1482.49030) Full Text: DOI
Amat, Sergio; Busquier, Sonia; Grau-Sánchez, Miquel; Hernández-Verón, M. A.; Rubio, M. J. On an inverse free Steffensen-type method for the approximation of stiff differential equations. (English) Zbl 1431.65091 Numer. Funct. Anal. Optim. 40, No. 2, 119-133 (2019). MSC: 65L04 65J15 PDFBibTeX XMLCite \textit{S. Amat} et al., Numer. Funct. Anal. Optim. 40, No. 2, 119--133 (2019; Zbl 1431.65091) Full Text: DOI
Petric, Mihaela; Zlatanov, Boyan Best proximity points for \(p\)-cyclic summing iterated contractions. (English) Zbl 1497.47083 Filomat 32, No. 9, 3275-3287 (2018). MSC: 47H10 47B10 41A65 PDFBibTeX XMLCite \textit{M. Petric} and \textit{B. Zlatanov}, Filomat 32, No. 9, 3275--3287 (2018; Zbl 1497.47083) Full Text: DOI
Samreen, Maria; Waheed, Khansa; Kiran, Quanita Multivalued \(\varphi\) contractions and fixed point theorems. (English) Zbl 1478.54110 Filomat 32, No. 4, 1209-1220 (2018). MSC: 54H25 54E40 65J15 45G99 PDFBibTeX XMLCite \textit{M. Samreen} et al., Filomat 32, No. 4, 1209--1220 (2018; Zbl 1478.54110) Full Text: DOI
Karakaya, Vatan; Doğan, Kadri; Atalan, Yunus; Bouzara, Nour El Houda The local and semilocal convergence analysis of new Newton-like iteration methods. (English) Zbl 1436.49038 Turk. J. Math. 42, No. 3, 735-751 (2018). Reviewer: Wiesław Kotarski (Sosnowiec) MSC: 49M15 65J15 47H10 PDFBibTeX XMLCite \textit{V. Karakaya} et al., Turk. J. Math. 42, No. 3, 735--751 (2018; Zbl 1436.49038) Full Text: DOI Link
Silva, G. N.; Santos, P. S. M.; Souza, S. S. Extended Newton-type method for nonlinear functions with values in a cone. (English) Zbl 1402.65047 Comput. Appl. Math. 37, No. 4, 5082-5097 (2018). MSC: 65J15 49M15 49M37 PDFBibTeX XMLCite \textit{G. N. Silva} et al., Comput. Appl. Math. 37, No. 4, 5082--5097 (2018; Zbl 1402.65047) Full Text: DOI
Domínguez Benavides, Tomás; Llorens-Fuster, Enrique Iterated nonexpansive mappings. (English) Zbl 06969095 J. Fixed Point Theory Appl. 20, No. 3, Paper No. 104, 18 p. (2018). MSC: 47H09 47H10 PDFBibTeX XMLCite \textit{T. Domínguez Benavides} and \textit{E. Llorens-Fuster}, J. Fixed Point Theory Appl. 20, No. 3, Paper No. 104, 18 p. (2018; Zbl 06969095) Full Text: DOI Link
Bernard, Séverine; Cabuzel, Catherine; Nuiro, Silvère Paul; Pietrus, Alain Extended semismooth Newton method for functions with values in a cone. (English) Zbl 1396.49022 Acta Appl. Math. 155, No. 1, 85-98 (2018). MSC: 49M15 49J53 47H04 65K10 14P15 PDFBibTeX XMLCite \textit{S. Bernard} et al., Acta Appl. Math. 155, No. 1, 85--98 (2018; Zbl 1396.49022) Full Text: DOI
Argyros, Ioannis K.; George, Santhosh On the convergence of Newton-like methods using restricted domains. (English) Zbl 1376.65087 Numer. Algorithms 75, No. 3, 553-567 (2017). Reviewer: Bangti Jin (London) MSC: 65J15 47J25 45G10 65R20 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. George}, Numer. Algorithms 75, No. 3, 553--567 (2017; Zbl 1376.65087) Full Text: DOI
Chen, Minhong; Wu, Qingbiao; Lin, Rongfei Semilocal convergence analysis for the modified Newton-HSS method under the Hölder condition. (English) Zbl 1343.65058 Numer. Algorithms 72, No. 3, 667-685 (2016). MSC: 65H10 PDFBibTeX XMLCite \textit{M. Chen} et al., Numer. Algorithms 72, No. 3, 667--685 (2016; Zbl 1343.65058) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd The majorant method in the theory of Newton-Kantorovich approximations and generalized Lipschitz conditions. (English) Zbl 1329.65114 J. Comput. Appl. Math. 291, 332-347 (2016). MSC: 65J15 47H10 49M15 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, J. Comput. Appl. Math. 291, 332--347 (2016; Zbl 1329.65114) Full Text: DOI
Argyros, I. K.; Khattri, S. K. Weak convergence conditions for the Newton’s method in Banach space using general majorizing sequences. (English) Zbl 1410.65208 Appl. Math. Comput. 263, 59-72 (2015). MSC: 65J15 49M15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. K. Khattri}, Appl. Math. Comput. 263, 59--72 (2015; Zbl 1410.65208) Full Text: DOI
Sahu, D. R.; Cho, Y. J.; Agarwal, R. P.; Argyros, I. K. Accessibility of solutions of operator equations by Newton-like methods. (English) Zbl 1320.65085 J. Complexity 31, No. 4, 637-657 (2015). MSC: 65J15 65Y20 PDFBibTeX XMLCite \textit{D. R. Sahu} et al., J. Complexity 31, No. 4, 637--657 (2015; Zbl 1320.65085) Full Text: DOI
Amat, S.; Hernández-Verón, M. A.; Rubio, M. J. Improving the applicability of the secant method to solve nonlinear systems of equations. (English) Zbl 1338.65136 Appl. Math. Comput. 247, 741-752 (2014). MSC: 65H10 39A60 PDFBibTeX XMLCite \textit{S. Amat} et al., Appl. Math. Comput. 247, 741--752 (2014; Zbl 1338.65136) Full Text: DOI
Singh, S. P.; Singh, M. R. Best approximation in nonlinear functional analysis. (English) Zbl 1317.41017 Ansari, Qamrul Hasan (ed.), Nonlinear analysis. Approximation theory, optimization and applications. Contributions based on the presentations at the special session on approximation theory and optimization in the Indian Mathematical Society conference, Varanasi, India, January 12–15, 2012. New Delhi: Birkhäuser/Springer (ISBN 978-81-322-1882-1/hbk; 978-81-322-1883-8/ebook). Trends in Mathematics, 165-198 (2014). MSC: 41A50 47H10 47J20 49J40 PDFBibTeX XMLCite \textit{S. P. Singh} and \textit{M. R. Singh}, in: Nonlinear analysis. Approximation theory, optimization and applications. Contributions based on the presentations at the special session on approximation theory and optimization in the Indian Mathematical Society conference, Varanasi, India, January 12--15, 2012. New Delhi: Birkhäuser/Springer. 165--198 (2014; Zbl 1317.41017) Full Text: DOI
Samreen, Maria; Kiran, Quanita; Kamran, Tayyab Fixed point theorems for \(\varphi\)-contractions. (English) Zbl 1489.54215 J. Inequal. Appl. 2014, Paper No. 266, 16 p. (2014). MSC: 54H25 47H10 54E40 PDFBibTeX XMLCite \textit{M. Samreen} et al., J. Inequal. Appl. 2014, Paper No. 266, 16 p. (2014; Zbl 1489.54215) Full Text: DOI
Sahu, D. R.; Singh, Krishna Kumar; Singh, Vipin Kumar A Newton-like method for generalized operator equations in Banach spaces. (English) Zbl 1307.65081 Numer. Algorithms 67, No. 2, 289-303 (2014). Reviewer: Zhihua Zhang (Beijing) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{D. R. Sahu} et al., Numer. Algorithms 67, No. 2, 289--303 (2014; Zbl 1307.65081) Full Text: DOI
Amat, Sergio; Argyros, Ioannis K.; Busquier, Sonia; Hilout, Saïd Expanding the applicability of high-order Traub-type iterative procedures. (English) Zbl 1308.65082 J. Optim. Theory Appl. 161, No. 3, 837-852 (2014). Reviewer: Vasile Postolică (Piatra Neamt) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{S. Amat} et al., J. Optim. Theory Appl. 161, No. 3, 837--852 (2014; Zbl 1308.65082) Full Text: DOI
Proinov, Petko D. A unified theory of cone metric spaces and its applications to the fixed point theory. (English) Zbl 1294.54035 Fixed Point Theory Appl. 2013, Paper No. 103, 38 p. (2013). MSC: 54H25 47H10 46A19 65J15 06F30 PDFBibTeX XMLCite \textit{P. D. Proinov}, Fixed Point Theory Appl. 2013, Paper No. 103, 38 p. (2013; Zbl 1294.54035) Full Text: DOI arXiv
Argyros, Ioannis K.; Hilout, Saïd On the quadratic convergence of Newton’s method under center-Lipschitz but not necessarily Lipschitz hypotheses. (English) Zbl 1349.65183 Math. Slovaca 63, No. 3, 621-638 (2013). Reviewer: Petko D. Proinov (Plovdiv) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, Math. Slovaca 63, No. 3, 621--638 (2013; Zbl 1349.65183) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd Extending the applicability of Newton’s method using nondiscrete induction. (English) Zbl 1274.65163 Czech. Math. J. 63, No. 1, 115-141 (2013). MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, Czech. Math. J. 63, No. 1, 115--141 (2013; Zbl 1274.65163) Full Text: DOI Link
Argyros, Ioannis K.; Hilout, Saïd Estimating upper bounds on the limit points of majorizing sequences for Newton’s method. (English) Zbl 1259.65080 Numer. Algorithms 62, No. 1, 115-132 (2013). MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, Numer. Algorithms 62, No. 1, 115--132 (2013; Zbl 1259.65080) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd New conditions for the convergence of Newton-like methods and applications. (English) Zbl 1309.65062 Appl. Math. Comput. 219, No. 6, 3279-3289 (2012). MSC: 65J15 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, Appl. Math. Comput. 219, No. 6, 3279--3289 (2012; Zbl 1309.65062) Full Text: DOI
Sahu, D. R.; Singh, Krishna Kumar; Singh, Vipin Kumar Some Newton-like methods with sharper error estimates for solving operator equations in Banach spaces. (English) Zbl 1273.49033 Fixed Point Theory Appl. 2012, Paper No. 78, 20 p. (2012). MSC: 49M15 47J25 47H09 47H10 65K10 PDFBibTeX XMLCite \textit{D. R. Sahu} et al., Fixed Point Theory Appl. 2012, Paper No. 78, 20 p. (2012; Zbl 1273.49033) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd Secant-type methods and nondiscrete induction. (English) Zbl 1267.65054 Numer. Algorithms 61, No. 3, 397-412 (2012). Reviewer: Otu Vaarmann (Tallinn) MSC: 65J15 47J15 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, Numer. Algorithms 61, No. 3, 397--412 (2012; Zbl 1267.65054) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd Majorizing sequences for iterative procedures in Banach spaces. (English) Zbl 1257.65026 J. Complexity 28, No. 5-6, 562-581 (2012). Reviewer: Peter Zabreiko (Minsk) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, J. Complexity 28, No. 5--6, 562--581 (2012; Zbl 1257.65026) Full Text: DOI
Ciarlet, Philippe G.; Mardare, Cristinel On the Newton-Kantorovich theorem. (English) Zbl 1308.65079 Anal. Appl., Singap. 10, No. 3, 249-269 (2012). MSC: 65J05 65J15 47J10 47J25 PDFBibTeX XMLCite \textit{P. G. Ciarlet} and \textit{C. Mardare}, Anal. Appl., Singap. 10, No. 3, 249--269 (2012; Zbl 1308.65079) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd Weaker conditions for the convergence of Newton’s method. (English) Zbl 1245.65058 J. Complexity 28, No. 3, 364-387 (2012). Reviewer: Hang Lau (Montréal) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, J. Complexity 28, No. 3, 364--387 (2012; Zbl 1245.65058) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd Majorizing sequences for iterative methods. (English) Zbl 1427.65090 J. Comput. Appl. Math. 236, No. 7, 1947-1960 (2012). MSC: 65J15 65H10 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, J. Comput. Appl. Math. 236, No. 7, 1947--1960 (2012; Zbl 1427.65090) Full Text: DOI
Ezquerro, J. A.; González, D.; Hernández, M. A. Majorizing sequences for Newton’s method from initial value problems. (English) Zbl 1241.65051 J. Comput. Appl. Math. 236, No. 9, 2246-2258 (2012). Reviewer: Michael M. Pahirya (Mukachevo) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{J. A. Ezquerro} et al., J. Comput. Appl. Math. 236, No. 9, 2246--2258 (2012; Zbl 1241.65051) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd Newton-Kantorovich approximations under weak continuity conditions. (English) Zbl 1291.65166 J. Appl. Math. Comput. 37, No. 1-2, 361-375 (2011). MSC: 65J15 65R20 49M15 45G10 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, J. Appl. Math. Comput. 37, No. 1--2, 361--375 (2011; Zbl 1291.65166) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd Extending the applicability of secant methods and nondiscrete induction. (English) Zbl 1251.65080 Appl. Math. Comput. 218, No. 7, 3238-3246 (2011). Reviewer: Juri M. Rappoport (Moskva) MSC: 65J15 47J25 45G10 65R20 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, Appl. Math. Comput. 218, No. 7, 3238--3246 (2011; Zbl 1251.65080) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd Weak convergence conditions for inexact Newton-type methods. (English) Zbl 1296.47065 Appl. Math. Comput. 218, No. 6, 2800-2809 (2011). MSC: 47J25 65J15 34B15 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, Appl. Math. Comput. 218, No. 6, 2800--2809 (2011; Zbl 1296.47065) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd A unified approach for the convergence of certain numerical algorithms, using recurrent functions. (English) Zbl 1214.65027 Computing 90, No. 3-4, 131-164 (2010). Reviewer: Werner H. Schmidt (Greifswald) MSC: 65J15 47J25 35J65 65N38 35C15 65H04 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, Computing 90, No. 3--4, 131--164 (2010; Zbl 1214.65027) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd Improved generalized differentiability conditions for Newton-like methods. (English) Zbl 1196.65100 J. Complexity 26, No. 3, 316-333 (2010). Reviewer: Erwin Schechter (Moers) MSC: 65J15 65L10 65R20 34B15 45G10 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, J. Complexity 26, No. 3, 316--333 (2010; Zbl 1196.65100) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd A convergence analysis of Newton-like method for singular equations using recurrent functions. (English) Zbl 1197.65056 Numer. Funct. Anal. Optim. 31, No. 2, 112-130 (2010). Reviewer: Peter Zabreiko (Minsk) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, Numer. Funct. Anal. Optim. 31, No. 2, 112--130 (2010; Zbl 1197.65056) Full Text: DOI
Proinov, Petko D. New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems. (English) Zbl 1185.65095 J. Complexity 26, No. 1, 3-42 (2010). Reviewer: Iulian Coroian (Baia Mare) MSC: 65J15 47J05 47H10 47J25 65H05 65E05 30C15 PDFBibTeX XMLCite \textit{P. D. Proinov}, J. Complexity 26, No. 1, 3--42 (2010; Zbl 1185.65095) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd On the convergence of Newton-type methods under mild differentiability conditions. (English) Zbl 1190.65091 Numer. Algorithms 52, No. 4, 701-726 (2009). Reviewer: Temur Jangveladze (Tbilisi) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, Numer. Algorithms 52, No. 4, 701--726 (2009; Zbl 1190.65091) Full Text: DOI
Bi, Weihong; Ren, Hongmin; Wu, Qingbiao Convergence analysis for the secant method based on new recurrence relations. (English) Zbl 1199.65184 Appl. Math., Ser. B (Engl. Ed.) 23, No. 4, 447-454 (2008). MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{W. Bi} et al., Appl. Math., Ser. B (Engl. Ed.) 23, No. 4, 447--454 (2008; Zbl 1199.65184) Full Text: DOI
Kiran, Quanita; Kamran, Tayyab Nadler’s type principle with high order of convergence. (English) Zbl 1220.54029 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 11, 4106-4120 (2008). Reviewer: Adrian Petruşel (Cluj-Napoca) MSC: 54H25 54C60 47H10 65J15 PDFBibTeX XMLCite \textit{Q. Kiran} and \textit{T. Kamran}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 11, 4106--4120 (2008; Zbl 1220.54029) Full Text: DOI
Wu, Min A convergence theorem for the Newton-like methods under some kind of weak Lipschitz conditions. (English) Zbl 1136.65059 J. Math. Anal. Appl. 339, No. 2, 1425-1431 (2008). Reviewer: Etienne Emmrich (Berlin) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{M. Wu}, J. Math. Anal. Appl. 339, No. 2, 1425--1431 (2008; Zbl 1136.65059) Full Text: DOI
Liang, Kewei Homocentric convergence ball of the secant method. (English) Zbl 1150.65015 Appl. Math., Ser. B (Engl. Ed.) 22, No. 3, 353-365 (2007). MSC: 65H10 PDFBibTeX XMLCite \textit{K. Liang}, Appl. Math., Ser. B (Engl. Ed.) 22, No. 3, 353--365 (2007; Zbl 1150.65015) Full Text: DOI
Ren, Hongmin An improved convergence theorem for a class of secant-like methods. (English) Zbl 1132.65050 Appl. Math. Comput. 189, No. 1, 472-481 (2007). Reviewer: Otu Vaarmann (Tallinn) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{H. Ren}, Appl. Math. Comput. 189, No. 1, 472--481 (2007; Zbl 1132.65050) Full Text: DOI
Proinov, Petko D. A generalization of the Banach contraction principle with high order of convergence of successive approximations. (English) Zbl 1130.54021 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 67, No. 8, 2361-2369 (2007). Reviewer: Zvonko Čerin (Zagreb) MSC: 54H25 47H10 65J15 65H10 PDFBibTeX XMLCite \textit{P. D. Proinov}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 67, No. 8, 2361--2369 (2007; Zbl 1130.54021) Full Text: DOI
Ren, Hongmin; Yang, Shijun; Wu, Qingbiao A new semilocal convergence theorem for the secant method under Hölder continuous divided differences. (English) Zbl 1112.65050 Appl. Math. Comput. 182, No. 1, 41-48 (2006). Reviewer: Erwin Schechter (Moers) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{H. Ren} et al., Appl. Math. Comput. 182, No. 1, 41--48 (2006; Zbl 1112.65050) Full Text: DOI
Ren, Hongmin; Wu, Qingbiao Mysovskii-type theorem for the Secant method under Hölder continuous Fréchet derivative. (English) Zbl 1094.65054 J. Math. Anal. Appl. 320, No. 1, 415-424 (2006). Reviewer: Mihai Turinici (Iaşi) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{H. Ren} and \textit{Q. Wu}, J. Math. Anal. Appl. 320, No. 1, 415--424 (2006; Zbl 1094.65054) Full Text: DOI
Argyros, Ioannis K. Weak sufficient convergence conditions and applications for Newton methods. (English) Zbl 1058.65059 J. Appl. Math. Comput. 16, No. 1-2, 1-17 (2004). Reviewer: W. C. Rheinboldt (Pittsburgh) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros}, J. Appl. Math. Comput. 16, No. 1--2, 1--17 (2004; Zbl 1058.65059) Full Text: DOI
Hernández, M. A.; Rubio, M. J. A modification of Newton’s method for nondifferentiable equations. (English) Zbl 1044.65045 J. Comput. Appl. Math. 164-165, 409-417 (2004). Reviewer: B. Döring (Düsseldorf) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{M. A. Hernández} and \textit{M. J. Rubio}, J. Comput. Appl. Math. 164--165, 409--417 (2004; Zbl 1044.65045) Full Text: DOI
Argyros, Ioannis K. An improved convergence analysis and applications for Newton-like methods in Banach space. (English) Zbl 1040.47045 Numer. Funct. Anal. Optimization 24, No. 7-8, 653-672 (2003). MSC: 47J25 65J15 90C55 PDFBibTeX XMLCite \textit{I. K. Argyros}, Numer. Funct. Anal. Optim. 24, No. 7--8, 653--672 (2003; Zbl 1040.47045) Full Text: DOI
Argyros, Ioannis K. An improved error analysis for Newton-like methods under generalized conditions. (English) Zbl 1030.65060 J. Comput. Appl. Math. 157, No. 1, 169-185 (2003). Reviewer: Yu Wenhuan (Tianjin) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros}, J. Comput. Appl. Math. 157, No. 1, 169--185 (2003; Zbl 1030.65060) Full Text: DOI
Hernández, M. A.; Rubio, M. J. Semilocal convergence of the secant method under mild convergence conditions of differentiability. (English) Zbl 1055.65069 Comput. Math. Appl. 44, No. 3-4, 277-285 (2002). MSC: 65J15 47J25 65L10 34B15 PDFBibTeX XMLCite \textit{M. A. Hernández} and \textit{M. J. Rubio}, Comput. Math. Appl. 44, No. 3--4, 277--285 (2002; Zbl 1055.65069) Full Text: DOI
Hernández, M. A.; Rubio, M. J. The secant method and divided differences Hölder continuous. (English) Zbl 1024.65043 Appl. Math. Comput. 124, No. 2, 139-149 (2001). MSC: 65J15 47J25 65L10 34B15 PDFBibTeX XMLCite \textit{M. A. Hernández} and \textit{M. J. Rubio}, Appl. Math. Comput. 124, No. 2, 139--149 (2001; Zbl 1024.65043) Full Text: DOI
Hernández, M. A. The Newton method for operators with Hölder continuous first derivative. (English) Zbl 1012.65052 J. Optimization Theory Appl. 109, No. 3, 631-648 (2001). Reviewer: S.I.Piskarev (Moskva) MSC: 65J15 47J25 45G10 65R20 PDFBibTeX XMLCite \textit{M. A. Hernández}, J. Optim. Theory Appl. 109, No. 3, 631--648 (2001; Zbl 1012.65052) Full Text: DOI
Gutiérrez, J. M.; Hernández, M. A. An application of Newton’s method to differential and integral equations. (English) Zbl 0976.65053 ANZIAM J. 42, No. 3, 372-386 (2001). Reviewer: W.C.Rheinboldt (Pittsburgh) MSC: 65J15 47J25 65L10 65R20 94B15 45E10 PDFBibTeX XMLCite \textit{J. M. Gutiérrez} and \textit{M. A. Hernández}, ANZIAM J. 42, No. 3, 372--386 (2001; Zbl 0976.65053) Full Text: DOI
Yamamoto, Tetsuro Historical developments in convergence analysis for Newton’s and Newton-like methods. (English) Zbl 0965.65079 J. Comput. Appl. Math. 124, No. 1-2, 1-23 (2000). Reviewer: Etienne Emmrich (Berlin) MSC: 65J15 47J25 65-03 PDFBibTeX XMLCite \textit{T. Yamamoto}, J. Comput. Appl. Math. 124, No. 1--2, 1--23 (2000; Zbl 0965.65079) Full Text: DOI
Hernández, M. A.; Rubio, M. J. A new type of recurrence relations for the secant method. (English) Zbl 0967.65073 Int. J. Comput. Math. 72, No. 4, 477-490 (1999). Reviewer: Aurel Galántai (Miskolc-Egyetemvaros) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{M. A. Hernández} and \textit{M. J. Rubio}, Int. J. Comput. Math. 72, No. 4, 477--490 (1999; Zbl 0967.65073) Full Text: DOI
Ezquerro, J. A.; Gutiérrez, J. M.; Hernández, M. A.; Salanova, M. A. Solving nonlinear integral equations arising in radiative transfer. (English) Zbl 0942.47043 Numer. Funct. Anal. Optimization 20, No. 7-8, 661-673 (1999). Reviewer: Jürgen Appell (Würzburg) MSC: 47H10 65J15 47G10 47J05 PDFBibTeX XMLCite \textit{J. A. Ezquerro} et al., Numer. Funct. Anal. Optim. 20, No. 7--8, 661--673 (1999; Zbl 0942.47043) Full Text: DOI
Hernández, M. A.; Salanova, M. A. Indices of convexity and concavity. Application to Halley method. (English) Zbl 0981.65071 Appl. Math. Comput. 103, No. 1, 27-49 (1999). MSC: 65J15 65H05 47J25 26A51 PDFBibTeX XMLCite \textit{M. A. Hernández} and \textit{M. A. Salanova}, Appl. Math. Comput. 103, No. 1, 27--49 (1999; Zbl 0981.65071) Full Text: DOI
Argyros, Ioannis K. On Newton’s method under mild differentiability conditions and applications. (English) Zbl 0930.65061 Appl. Math. Comput. 102, No. 2-3, 177-183 (1999). Reviewer: K.Najzar (Praha) MSC: 65J15 47J25 45G10 65R20 PDFBibTeX XMLCite \textit{I. K. Argyros}, Appl. Math. Comput. 102, No. 2--3, 177--183 (1999; Zbl 0930.65061) Full Text: DOI
Ezquerro, J. A.; Hernández, M. A. On a convex acceleration of Newton’s method. (English) Zbl 0915.90235 J. Optimization Theory Appl. 100, No. 2, 311-326 (1999). MSC: 90C30 65H10 PDFBibTeX XMLCite \textit{J. A. Ezquerro} and \textit{M. A. Hernández}, J. Optim. Theory Appl. 100, No. 2, 311--326 (1999; Zbl 0915.90235) Full Text: DOI
Hernández, M. A.; Salanova, M. A. Chebyshev method and convexity. (English) Zbl 0943.65071 Appl. Math. Comput. 95, No. 1, 51-62 (1998). MSC: 65J15 47J25 65H05 PDFBibTeX XMLCite \textit{M. A. Hernández} and \textit{M. A. Salanova}, Appl. Math. Comput. 95, No. 1, 51--62 (1998; Zbl 0943.65071) Full Text: DOI
Chen, X.; Qi, L.; Sun, D. Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities. (English) Zbl 0894.90143 Math. Comput. 67, No. 222, 519-540 (1998). MSC: 90C33 65H10 90C30 49J40 PDFBibTeX XMLCite \textit{X. Chen} et al., Math. Comput. 67, No. 222, 519--540 (1998; Zbl 0894.90143) Full Text: DOI
Argyros, Ioannis K. A mesh independence principle for inexact Newton-like methods and their discretizations under generalized Lipschitz conditions. (English) Zbl 0908.65043 Appl. Math. Comput. 87, No. 1, 15-48 (1997). Reviewer: V.Berinde (Baia Mare) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros}, Appl. Math. Comput. 87, No. 1, 15--48 (1997; Zbl 0908.65043) Full Text: DOI
Ezquerro, J. A.; Gutiérrez, J. M.; Hernández, M. A. A construction procedure of iterative methods with cubical convergence. (English) Zbl 0879.65035 Appl. Math. Comput. 85, No. 2-3, 181-199 (1997). Reviewer: E.Emmrich (Magdeburg) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{J. A. Ezquerro} et al., Appl. Math. Comput. 85, No. 2--3, 181--199 (1997; Zbl 0879.65035) Full Text: DOI
Gutiérrez, J. M.; Hernández, M. A. A family of Chebyshev-Halley type methods in Banach spaces. (English) Zbl 0893.47043 Bull. Aust. Math. Soc. 55, No. 1, 113-130 (1997). MSC: 47J25 47H10 65J15 PDFBibTeX XMLCite \textit{J. M. Gutiérrez} and \textit{M. A. Hernández}, Bull. Aust. Math. Soc. 55, No. 1, 113--130 (1997; Zbl 0893.47043) Full Text: DOI
Chen, Xiaojun Superlinear convergence of smoothing quasi-Newton methods for nonsmooth equations. (English) Zbl 0881.65042 J. Comput. Appl. Math. 80, No. 1, 105-126 (1997). Reviewer: B.Döring (Düsseldorf) MSC: 65H10 65K10 49J40 49M25 PDFBibTeX XMLCite \textit{X. Chen}, J. Comput. Appl. Math. 80, No. 1, 105--126 (1997; Zbl 0881.65042) Full Text: DOI
Gutiérrez, José M. A new semilocal convergence theorem for Newton’s method. (English) Zbl 0872.65045 J. Comput. Appl. Math. 79, No. 1, 131-145 (1997). Reviewer: W.H.Schmidt (Greifswald) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{J. M. Gutiérrez}, J. Comput. Appl. Math. 79, No. 1, 131--145 (1997; Zbl 0872.65045) Full Text: DOI
Ezquerro, J. A.; Hernández, M. A. A note on a family of Newton type iterative processes. (English) Zbl 0871.65038 Int. J. Comput. Math. 62, No. 3-4, 223-232 (1996). Reviewer: B.Döring (Düsseldorf) MSC: 65H05 65E05 PDFBibTeX XMLCite \textit{J. A. Ezquerro} and \textit{M. A. Hernández}, Int. J. Comput. Math. 62, No. 3--4, 223--232 (1996; Zbl 0871.65038) Full Text: DOI
Galperin, A.; Waksman, Z. Newton-type methods under regular smoothness. (English) Zbl 0865.65041 Numer. Funct. Anal. Optimization 17, No. 3-4, 259-291 (1996). Reviewer: V.Berinde (Baia Mare) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{A. Galperin} and \textit{Z. Waksman}, Numer. Funct. Anal. Optim. 17, No. 3--4, 259--291 (1996; Zbl 0865.65041) Full Text: DOI
Gutiérrez, J. M.; Hernández, M. A.; Salanova, M. A. Resolution of quadratic equations in Banach spaces. (English) Zbl 0849.47038 Numer. Funct. Anal. Optimization 17, No. 1-2, 113-121 (1996). MSC: 47J25 65J15 PDFBibTeX XMLCite \textit{J. M. Gutiérrez} et al., Numer. Funct. Anal. Optim. 17, No. 1--2, 113--121 (1996; Zbl 0849.47038) Full Text: DOI
Hernández, M. A.; Salanova, M. A. A family of Newton type iterative processes. (English) Zbl 0824.65025 Int. J. Comput. Math. 51, No. 3-4, 205-214 (1994). MSC: 65H05 26A51 PDFBibTeX XMLCite \textit{M. A. Hernández} and \textit{M. A. Salanova}, Int. J. Comput. Math. 51, No. 3--4, 205--214 (1994; Zbl 0824.65025) Full Text: DOI
Hernández, M. A.; Salanova, M. A. A family of Chebyshev-Halley type methods. (English) Zbl 0812.65038 Int. J. Comput. Math. 47, No. 1-2, 59-63 (1993). MSC: 65H05 PDFBibTeX XMLCite \textit{M. A. Hernández} and \textit{M. A. Salanova}, Int. J. Comput. Math. 47, No. 1--2, 59--63 (1993; Zbl 0812.65038) Full Text: DOI
Chen, Xiaojun; Yamamoto, Tetsuro A convergence ball for multistep simplified Newton-like methods. (English) Zbl 0801.65052 Numer. Funct. Anal. Optimization 14, No. 1-2, 15-24 (1993). MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{X. Chen} and \textit{T. Yamamoto}, Numer. Funct. Anal. Optim. 14, No. 1--2, 15--24 (1993; Zbl 0801.65052) Full Text: DOI Link
Zhang, L.-Q.; Han, G.-Q. Optimal homotopy methods for solving nonlinear systems. I: Nonsingular homotopy paths. (English) Zbl 0797.65045 Numer. Math. 65, No. 4, 523-538 (1993). Reviewer: Wang Zeke (Guangzhou) MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{L. Q. Zhang} and \textit{G. Q. Han}, Numer. Math. 65, No. 4, 523--538 (1993; Zbl 0797.65045) Full Text: DOI EuDML
Rheinboldt, Werner C. On the theory and error estimation of the reduced basis method for multi- parameter problems. (English) Zbl 0802.65068 Nonlinear Anal., Theory Methods Appl. 21, No. 11, 849-858 (1993). Reviewer: Yu Wenhuan (Tianjin) MSC: 65H17 PDFBibTeX XMLCite \textit{W. C. Rheinboldt}, Nonlinear Anal., Theory Methods Appl. 21, No. 11, 849--858 (1993; Zbl 0802.65068) Full Text: DOI
Argyros, I. K. Some methods for finding error bounds for Newton-like methods under mild differentiability conditions. (English) Zbl 0816.65033 Acta Math. Hung. 61, No. 3-4, 183-194 (1993). Reviewer: W.C.Rheinboldt (Pittsburgh) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros}, Acta Math. Hung. 61, No. 3--4, 183--194 (1993; Zbl 0816.65033) Full Text: DOI
Huang, Zhengda A note on the Kantorovich theorem for Newton iteration. (English) Zbl 0782.65071 J. Comput. Appl. Math. 47, No. 2, 211-217 (1993). Reviewer: Z.Mei (Marburg) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{Z. Huang}, J. Comput. Appl. Math. 47, No. 2, 211--217 (1993; Zbl 0782.65071) Full Text: DOI
Argyros, Ioannis K. On an application of a Newton-like method to the approximation of implicit functions. (English) Zbl 0771.47035 Math. Slovaca 42, No. 3, 339-347 (1992). Reviewer: D.Werner (Berlin) MSC: 47J25 47L05 65J15 46G05 PDFBibTeX XMLCite \textit{I. K. Argyros}, Math. Slovaca 42, No. 3, 339--347 (1992; Zbl 0771.47035) Full Text: EuDML
Argyros, Ioannis K. Some generalized projection methods for solving operator equations. (English) Zbl 0747.65038 J. Comput. Appl. Math. 39, No. 1, 1-6 (1992). Reviewer: Simeon Reich (Los Angeles) MSC: 65J15 65R20 47J25 45G10 PDFBibTeX XMLCite \textit{I. K. Argyros}, J. Comput. Appl. Math. 39, No. 1, 1--6 (1992; Zbl 0747.65038) Full Text: DOI
Argyros, Ioannis K. Sharp error bounds for Newton-like methods under weak smoothness assumptions. (English) Zbl 0771.47034 Bull. Aust. Math. Soc. 45, No. 3, 415-422 (1992). Reviewer: D.Werner (Berlin) MSC: 47J25 65J15 47L05 PDFBibTeX XMLCite \textit{I. K. Argyros}, Bull. Aust. Math. Soc. 45, No. 3, 415--422 (1992; Zbl 0771.47034) Full Text: DOI
Argyros, Ioannis K. Some projection methods for the approximation of implicit functions. (English) Zbl 0722.65030 Appl. Math. Lett. 3, No. 2, 5-7 (1990). Reviewer: Simeon Reich (Los Angeles) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros}, Appl. Math. Lett. 3, No. 2, 5--7 (1990; Zbl 0722.65030) Full Text: DOI
Zufiria, Pedro J.; Guttalu, Ramesh S. On an application of dynamical systems theory to determine all the zeros of a vector function. (English) Zbl 0722.65029 J. Math. Anal. Appl. 152, No. 1, 269-295 (1990). Reviewer: I.N.Molchanov (Kiev) MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{P. J. Zufiria} and \textit{R. S. Guttalu}, J. Math. Anal. Appl. 152, No. 1, 269--295 (1990; Zbl 0722.65029) Full Text: DOI
Chen, X. On the convergence of Broyden-like methods for nonlinear equations with nondifferentiable terms. (English) Zbl 0718.65039 Ann. Inst. Stat. Math. 42, No. 2, 387-401 (1990). Reviewer: A.Varga (Bucureşti) MSC: 65H10 PDFBibTeX XMLCite \textit{X. Chen}, Ann. Inst. Stat. Math. 42, No. 2, 387--401 (1990; Zbl 0718.65039) Full Text: DOI
Argyros, Ioannis K. The Newton-Kantorovich method under mild differentiability conditions and the Ptâk error estimates. (English) Zbl 0712.65053 Monatsh. Math. 109, No. 3, 175-193 (1990). Reviewer: Ioannis K.Argyros MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros}, Monatsh. Math. 109, No. 3, 175--193 (1990; Zbl 0712.65053) Full Text: DOI EuDML
Zufiria, Pedro J.; Guttalu, Ramesh S. A computational method for finding all the roots of a vector function. (English) Zbl 0706.65045 Appl. Math. Comput. 35, No. 1, 13-59 (1990). Reviewer: Chengxian Xu MSC: 65H10 65H20 58C30 PDFBibTeX XMLCite \textit{P. J. Zufiria} and \textit{R. S. Guttalu}, Appl. Math. Comput. 35, No. 1, 13--59 (1990; Zbl 0706.65045) Full Text: DOI
Yamamoto, Tetsuro; Chen, Xiaojun Ball-convergence theorems and error estimates for certain iterative methods for nonlinear equations. (English) Zbl 0699.65042 Japan J. Appl. Math. 7, No. 1, 131-143 (1990). Reviewer: J.Kolomý MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{T. Yamamoto} and \textit{X. Chen}, Japan J. Appl. Math. 7, No. 1, 131--143 (1990; Zbl 0699.65042) Full Text: DOI
Moret, Igor A Kantorovich-type theorem for inexact Newton methods. (English) Zbl 0653.65044 Numer. Funct. Anal. Optimization 10, No. 3-4, 351-365 (1989). Reviewer: I.Moret MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. Moret}, Numer. Funct. Anal. Optim. 10, No. 3--4, 351--365 (1989; Zbl 0653.65044) Full Text: DOI
Chen, Xiaojun; Yamamoto, Tetsuro Convergence domains of certain iterative methods for solving nonlinear equations. (English) Zbl 0645.65028 Numer. Funct. Anal. Optimization 10, No. 1-2, 37-48 (1989). Reviewer: Xiaojun Chen MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{X. Chen} and \textit{T. Yamamoto}, Numer. Funct. Anal. Optim. 10, No. 1--2, 37--48 (1989; Zbl 0645.65028) Full Text: DOI
Argyros, Ioannis K. On Newton’s method and nondiscrete mathematical induction. (English) Zbl 0642.65043 Bull. Aust. Math. Soc. 38, No. 1, 131-140 (1988). Reviewer: O.Hadžić MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros}, Bull. Aust. Math. Soc. 38, No. 1, 131--140 (1988; Zbl 0642.65043) Full Text: DOI
Moret, Igor On a general iterative scheme for Newton-type methods. (English) Zbl 0635.65069 Numer. Funct. Anal. Optimization 9(1987-88), No. 11-12, 1115-1137 (1988). Reviewer: I.Moret MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. Moret}, Numer. Funct. Anal. Optim. 9, 1115--1137 (1987; Zbl 0635.65069) Full Text: DOI
Yamamoto, Tetsuro A convergence theorem for Newton-like methods in Banach spaces. (English) Zbl 0633.65049 Numer. Math. 51, 545-557 (1987). Reviewer: J.Kolomý MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{T. Yamamoto}, Numer. Math. 51, 545--557 (1987; Zbl 0633.65049) Full Text: DOI EuDML