The solvability of a class of system of nonlinear integral equations via measure of noncompactness

Abstract

We propose a new notion of contraction mappings for two class of functions involving measure of noncompactness in Banach space. In this regard we present some theory and results on the existence of tripled fixed points and some basic Darbo's type fixed points for a class of operators in Banach spaces. Also as an application we discuss the existence of solutions for a general system of nonlinear functional integral equations which satisfy in new certain conditions. Further we give an example to verify the effectiveness and applicability of our results.

An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

“…Here we use the methodology of MNC to enlarge the Darbo fixed point theorem [16]. Our goal is extending the results of [3] from two dimensions to three dimensions and the results of [30] on the existence of three-dimensional fixed points and tripled fixed points for a class of operators in a Banach space.…”