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.


45G10 Other nonlinear integral equations
47H08 Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
47H10 Fixed-point theorems
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
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