Fixed Point Theorems for Weakly Asymptotically Regular Mappings in Banach Spaces with an Application

Abstract

Using the technique of measures of weak non-compactness we obtain the existence of fixed points of a 2 × 2 block operator matrix involving nonlinear maps in non-separable Banach space. These theorems are created in terms of weak sequential continuity and the theory of countably condensing maps. Our results generalize, improve and complement a number of earlier works. The obtained results are then applied to a coupled system of nonlinear functional integral equations.