New classes of condensing operators and application to solvability of singular integral equations

Abstract

In this paper, we introduce the notion of Krasnoselskii and Dugundji-Granas condensing operators in Banach spaces. In order to pave the way for a study the solvability of some classes of singular integral equations in the Banach algebra $C[a,b]$, we provide some results forthe existence of fixed points for such condensing operators. An example is presented to show the applicability of the results.