Sadovskii-Krasnoselskii type fixed point theorems in Banach spaces with application to evolution equations
In this work, we introduce the concept of a convex-power condensing mapping \(T\) with respect to another mapping \(S\) as a generalization of condensing and convex-power condensing mappings. Some fixed point theorems for the sum \(T+S\) with \(S\) is a strict contraction and \(T\) is convex-power condensing with respect to \(S\) are established. The cases where \(S\) is nonexpansive or expansive are also considered. Our fixed point results encompass the well known Sadovskiis fixed point theorem and a number of its generalizations. To show the usefulness and the applicability of our fixed point results we investigate the existence of mild solutions to a broad class of neutral differential equations.
sadovskii-krasnoselskii type fixed point theorems neutral differential equation measure of noncompactness semigroups nonexpansive maps 47h10 47h08 47d06 47g10 31b10