Some fixed point theorems for Meir-Keeler condensing operators and application to a system of integral equations

Abstract

We introduce the concept of Meir-Keeler condensing operator in a Banach space via an arbitrary measure of weak noncompactness. We prove some generalizations of Darbo's fixed point theorem by considering a measure of weak noncompactness which not necessary has the maximum property. We prove some coupled fixed point theorems and we apply them in order to establish the existence of weak solutions for a system of functional integral equations of Volterra type.