Measure of noncompactness and a generalized Darbo's fixed point theorem and its applications to a system of integral equations

Abstract

Isik et al. (Mathematics 7:862,2019) presented an interesting generalization of the Banach contraction principle. In this paper, motivated by Isik et al., we give a new extension of the well-known Darbo inequality in a Banach space. Our results provide several generalizations of the Darbo inequality. As an application, we study the existence of solutions for a system of functional integral equations inC[0,T]. Finally, we expose a genuine example to support the effectiveness of our results.