Krasnosel’skii-type fixed point theorems with applications to Volterra integral equations

Abstract

In this paper we present some fixed point results for the sum S + T of two mappings where S is a strict contraction and T is not necessarily weakly compact and satisfies a new condition formulated in terms of an axiomatic measure of weak noncompactness. Our fixed point results extend and improve several earlier results in the literature. In particular, our results encompass the analogues of Krasnosel'skii's and Sadovskii's fixed point theorems for sequentially weakly continuous mappings and a number of their generalizations. Finally, an application to integral equations is given to illustrate the usability of the obtained results.