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Integrable solutions of a nonlinear functional integral equation on an unbounded interval. (English) Zbl 1203.45004
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 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 [J. Banas and 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.

45G10Nonsingular nonlinear integral equations
47H08Measures of noncompactness and condensing mappings, K-set contractions, etc.
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H30Particular nonlinear operators