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.