Integrable solutions of a nonlinear functional integral equation on an unbounded interval

In this paper we prove the existence of integrable solutions of a generalized functional-integral equation, which includes many key integral and functional equations that arise in nonlinear analysis and its applications. This is achieved by means of an improvement of a Krasnosel’skii type fixed poin...

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Bibliographic Details
Published in:Nonlinear analysis 2009-11, Vol.71 (9), p.4131-4136
Main Author: Aziz Taoudi, Mohamed
Format: Article
Language:English
Subjects:
Difference and functional equations, recurrence relations
Exact sciences and technology
Finite differences and functional equations
Fixed point theorem
Functional integral equation
Global analysis, analysis on manifolds
Integral equations
Mathematical analysis
Mathematics
Measure of weak noncompactness
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Superposition operator
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:In this paper we prove the existence of integrable solutions of a generalized functional-integral equation, which includes many key integral and functional equations that arise in nonlinear analysis and its applications. This is achieved by means of an improvement of a Krasnosel’skii type fixed point theorem recently proved by K. Latrach and the author. The result presented in this paper extends the corresponding result of [J. Banas, A. Chlebowicz, On existence of integrable solutions of a functional integral equation under Carathéodory condition, Nonlinear Anal. (2008) doi:10.1016/j.na.2008.04.020]. An example which shows the importance and the applicability of our result is also included.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2009.02.072