zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Fixed point theorems in the Fréchet space 𝒞( + ) and functional integral equations on an unbounded interval. (English) Zbl 1245.45006
Summary: We establish fixed point theorems for operators in the Fréchet space of continuous functions on the real half-axis. In our considerations we apply the technique of measures of noncompactness in conjunction with the Tikchonov fixed point theorem. The obtained results are applied in the proof of the solvability of a nonlinear functional integral equation with the initial value. Moreover, we show that solutions of that equation are uniformly globally asymptotically attractive. The results presented in the paper allow to improve existence theorems for integral and functional equations obtained earlier in many research papers.
MSC:
45G10Nonsingular nonlinear integral equations
References:
[1]Aghajani, A.; Jalilian, Y.: Existence and global attractivity of solutions of a nonlinear functional integral equation, Commun. nonlinear sci. Numer. simulat. 15, 3306-3312 (2010) · Zbl 1222.45004 · doi:10.1016/j.cnsns.2009.12.035
[2]Balahandran, K.; Park, J. Y.; Julie, M. Diana: On local attractivity of solutions of a functional integral equation of fractional order with deviating arguments, Commun. nonlinear sci. Numer. simulat. 15, 2809-2817 (2010) · Zbl 1222.45002 · doi:10.1016/j.cnsns.2009.11.023
[3]Banaś, J.; Balachandran, K.; Julie, D.: Existence and global attractivity of solutions of a nonlinear functional integral equation, Appl. math. Comput. 216, 261-268 (2010) · Zbl 1191.45004 · doi:10.1016/j.amc.2010.01.049
[4]Banaś, J.; Dhage, B. C.: Global asymptotic stability of solutions of a functional integral equation, Nonlinear anal. 69, 1945-1952 (2008) · Zbl 1154.45005 · doi:10.1016/j.na.2007.07.038
[5]Banaś, J.; Martin, J. R.; Sadarangani, K.: On solutions of a quadratic integral equation of Hammerstein type, Math. comput. Model. 43, 97-104 (2006) · Zbl 1098.45003 · doi:10.1016/j.mcm.2005.04.017
[6]Banaś, J.; Rocha, J.; Sadarangani, K.: Solvability of a nonlinear integral equation of Volterra type, J. comput. Appl. math. 157, 31-48 (2003) · Zbl 1026.45006 · doi:10.1016/S0377-0427(03)00373-X
[7]Banaś, J.; O’regan, D.: On existence and local attractivity of solutions of a quadratic Volterra integral equation of fractional order, J. math. Anal. appl. 345, 573-582 (2008) · Zbl 1147.45003 · doi:10.1016/j.jmaa.2008.04.050
[8]Banaś, J.; Rzepka, B.: On local attractivity and asymptotic stability of solutions af a quadratic Volterra integral equation, Appl. math. Comput. 213, 102-111 (2009) · Zbl 1175.45002 · doi:10.1016/j.amc.2009.02.048
[9]Banaś, J.; Rzepka, B.: On existence and asymptotic stability of solutions of a nonlinear integral equation, J. math. Anal. appl. 284, 165-173 (2003) · Zbl 1029.45003 · doi:10.1016/S0022-247X(03)00300-7
[10]Banaś, J.; Rzepka, B.: An application of a measure of noncompactness in the study of asymptotic stability, Appl. math. Lett. 16, 1-6 (2003) · Zbl 1015.47034 · doi:10.1016/S0893-9659(02)00136-2
[11]Banaś, J.; Zaja&cedil, T.; C: Solvability of a functional integral equation of fractional order in the class of functions having limits at infinity, Nonlinear anal. 71, 5491-5500 (2009)
[12]Caballero, J.; O’regan, D.; Sadarangani, K.: On solutions of an integral equation related to traffic flow on unbounded domains, Arch. math. 82, 551-563 (2004) · Zbl 1059.45003 · doi:10.1007/s00013-003-0609-3
[13]Dhage, B. C.; Lakshmikantham, V.: On global existence and attractivity results for nonlinear functional integral equations, Nonlinear anal. 72, 2219-2227 (2010) · Zbl 1197.45005 · doi:10.1016/j.na.2009.10.021
[14]Dhage, B. C.: Asymptotic stability of nonlinear functional integral equations via measures of noncompactness, Commun. appl. Nonlinear anal. 15, No. 2, 89-101 (2008) · Zbl 1160.47041
[15]Hu, X.; Yan, J.: The global attractivity and asymptotic stability of solution of a nonlinear integral equation, J. math. Anal. appl. 321, 147-156 (2006) · Zbl 1108.45006 · doi:10.1016/j.jmaa.2005.08.010
[16]Banaś, J.; Cabrera, I. J.: On solutions of a neutral differential equation with deviating argument, Math. comput. Model. 44, 1080-1088 (2006) · Zbl 1187.34109 · doi:10.1016/j.mcm.2006.03.012
[17]Banaś, J.; Cabrera, I. J.: On existence and asymptotic behaviour of solutions of a functional integral equation, Nonlinear anal. 66, 2246-2254 (2007) · Zbl 1128.45004 · doi:10.1016/j.na.2006.03.015
[18]El-Sayed, W. G.: Solvability of a neutral differential equation with deviated argument, J. math. Anal. appl. 327, 342-350 (2007) · Zbl 1115.34076 · doi:10.1016/j.jmaa.2006.04.023
[19]Banaś, J.; Goebel, K.: Measures of noncomapctness in Banach spaces, Lecture notes in pure and applied math 60 (1980) · Zbl 0441.47056
[20]Olszowy, L.: On existence of solutions of a quadratic Urysohn integral equation on an unbounded interval, Comment. math. 46, No. 1, 103-112 (2008) · Zbl 1179.45005
[21]Dhage, B. C.: Asymptotic stability of nonlinear functional integral equations via measures of noncompactness, Commun. appl. Nonlinear anal. 15, No. 2, 89-101 (2008) · Zbl 1160.47041
[22]Agarwal, R. P.; O’regan, D.: Infinite interval problems for differential, Difference and integral equations (2001)