A generalization of Krasnosel'skii compression fixed point theorem by using star convex sets

Abstract

In the framework of fixed point theory, many generalizations of the classical results due to Krasnosel'skii are known. One of these extensions consists in relaxing the conditions imposed on the mapping, working with k-set contractions instead of continuous and compact maps. The aim of this work if to study in detail some fixed point results of this type, and obtain a certain generalization by using star convex sets.

Existence of positive solutions of a Hammerstein integral equation using the layered compression-expansion fixed point theorem

“…In this paper, we show that under the same assumptions on the kernel G, the Layered Expansion-Compression Fixed Point Theorem can be applied to show the existence of positive and positive symmetric solutions of the Hammerstein integral equation. More examples of recent work on Hammerstein integral equations, can be found in [14,15,19,21,26].…”