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Zbl 1203.45004
Taoudi, Mohamed Aziz
Integrable solutions of a nonlinear functional integral equation on an unbounded interval. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 9, A, 4131-4136 (2009). ISSN 0362-546X

Summary: 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 {\it K.\,Latrach} and the author [Nonlinear Anal., Theory Methods Appl.\ 66, No.\,10, A, 2325--2333 (2007; Zbl 1128.45006)]. The result presented in this paper extends the corresponding result of [{\it J.\,Banas} and {\it A.\,Chlebowicz}, ibid.\ 70, No.\,9, A, 3172--3179 (2009; Zbl 1168.45005)]. An example which shows the importance and the applicability of our result is also included.

MSC 2000:: *45G10 Nonsingular nonlinear integral equations
47H08
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H30 Particular nonlinear operators

Keywords: fixed point theorem; measure of weak noncompactness; functional integral equation; superposition operator

Citations: Zbl 1128.45006; Zbl 1168.45005

Cited in: Zbl pre06110329

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