Some Krasnosel’skii-type fixed point theorems for Meir–Keeler-type mappings

Abstract

In this paper, inspired by the idea of Meir-Keeler contractive mappings, we introduce Meir-Keeler expansive mappings, say MKE, in order to obtain Krasnosel'skii-type fixed point theorems in Banach spaces. The idea of the paper is to combine the notion of Meir-Keeler mapping and expansive Krasnosel'skii fixed point theorem. We replace the expansion condition by the weakened MKE condition in some variants of Krasnosel'skii fixed point theorems

Fixed Points of Generalized α -Meir-Keeler Contraction Mappings in S b

“…Pourhadi et al [2] introduced the concept of Meir-Keeler expansive mappings and obtained Krasnosel'skiitype fixed point theorem in Banach spaces. A new fixed point theorem was obtained by Du and Rassias [3] for a Meir-Keeler type condition as a generalization of the Banach contraction principle, Kannan's fixed point theorem, Chatterjea's fixed point theorem, etc., simultaneously.…”