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CALOGERO VETRO

A New Extension of Darbo's Fixed Point Theorem Using Relatively Meir-Keeler Condensing Operators

Abstract

We consider relatively Meir-Keeler condensing operators to study the existence of best proximity points (pairs) by using the notion of measure of noncompactness, and extend a result of Aghajani et al. ['Fixed point theorems for Meir-Keeler condensing operators via measure of noncompactness', Acta Math. Sci. Ser. B 35 (2015), 552-566]. As an application of our main result, we investigate the existence of an optimal solution for a system of integrodifferential equations.