On an integral equation under Henstock–Kurzweil–Pettis integrability

Abstract

In this paper, we investigate the set of solutions for nonlinear Volterra type integral equations in Banach spaces in the weak sense and under Henstock-Kurzweil-Pettis integrability. Moreover, a fixed point result is presented for weakly sequentially continuous mappings defined on the function space C(K , X ), where K is compact Hausdorff and X is a Banach space. The main condition is expressed in terms of axiomatic measure of weak noncompactness. Mathematics Subject Classification

Fixed Points for Sum or Product of Operators in Weak Topology With Applications (A Survey) H. H. G. Hashem

“…In 2015, A. B. Amar [10] investigated the set of solutions for nonlinear Volterra type integral equations in Banach spaces in the weak sense and under Henstock-Kurzweil-Pettis integrability. Moreover, a fixed point result was presented for weakly sequentially continuous mappings defined on the function space C(K, X), where K is compact Hausdorff and X is a Banach space.…”