Existence of Solutions for a Nonlinear Integral Equation via a Hybrid Fixed Point Theorem

Abstract

This paper is devoted to prove the existence of continuous solutions for a nonlinear integral equation. Our existence theorem extends in a broad sense the analogous one obtained by L.T.P. Ngoc and N.T. Long. To this aim we first prove new variants of the Krasnosel’skii–Sadowskii and of the Krasnosel’skii–Daher fixed point theorems in Hausdorff locally convex topological vector spaces. These hybrid theorems improve some recently obtained results. Moreover a fixed point theorem for a multimap defined on a cartesian product subset of a Banach space is stated.