Some Krasnosel’skii-type fixed point theorems for Meir–Keeler-type mappings
Articles
Ehsan Pourhadi
Linnæus University
https://orcid.org/0000-0003-3056-4299
Reza Saadati
Iran University of Science and Technology
https://orcid.org/0000-0002-6770-6951
Zoran Kadelburg
University of Belgrade
https://orcid.org/0000-0001-9103-713X
Published 2020-03-02
https://doi.org/10.15388/namc.2020.25.16516
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Keywords

Meir–Keeler expansive
Meir–Keeler contractive
Krasnosel’skii fixed point theorem

How to Cite

Pourhadi, E., Saadati, R. and Kadelburg, Z. (2020) “Some Krasnosel’skii-type fixed point theorems for Meir–Keeler-type mappings”, Nonlinear Analysis: Modelling and Control, 25(2), pp. 257–265. doi:10.15388/namc.2020.25.16516.

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 that appear in the literature, e.g., in [T. Xiang, R. Yuan, A class of expansive-type Krasnosel’skii fixed point theorems, Nonlinear Anal., Theory Methods Appl., 71(7–8):3229–3239, 2009].

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