Applications of measure of non-compactness and modified simulation function for solvability of nonlinear functional integral equations

Abstract

In this work we introduce a modified version of simulation function and define a simulation type contraction mappings involving measure of non-compactness in the frame work of Banach space and derive some basic Darbo type fixed point results. Also, our theorem generalizes the Theorem 4 of [R. Arab, Some generalizations of Darbo fixed point theorem and its application, Miskolc Mathematical Notes, 18(2)(2017),595-610.] and extend some recent results. Further we show the applicability of obtained results to the theory of integral equations followed by two concrete examples.