Fixed point theorem via measure of noncompactness and application to Volterra integral equations in Banach algebras

Abstract

We propose a new notion of contraction mappings for two class of functions involving measure of noncompactness in Banach space and derive some basic Darbo type fixed and coupled fixed point results. This work includes and extends the results of Falset and Latrach[ Falset, J. G., Latrach, K. : On Darbo-Sadovskii's fixed point theorems type for abstract measures of (weak) noncompactness, Bull. Belg. Math. Soc. Simon Stevin 22 (2015), 797-812.] The results are also correlated with the classical generalized Banach fixed point theorems. Also we show the applicability of obtained results to the Volterra integral equations in Banach algebras.