On approximating fixed points of strictly pseudocontractive mappings in metric spaces

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Publication Details

Author list: Salisu, Sani; Berinde, Vasile; Sriwongsa, Songpon; Kumam, Poom

Publication year: 2024

Journal: Carpathian Journal of Mathematics (1843-4401)

Volume number: 40

Issue number: 2

Start page: 419

End page: 430

Number of pages: 12

ISSN: 1843-4401

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85190945062&doi=10.37193%2fCJM.2024.02.12&partnerID=40&md5=a61ddc1107fa1360b61c717d0effed60

Languages: English-Great Britain (EN-GB)

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Abstract

In this work, we analyse the class of strictly pseudocontractive mappings in general metric spaces by providing a comprehensive and appropriate definition of a strictly pseudocontractive mapping, which serves as a natural extension of the existing notion. Moreover, we establish its various characterizations and explore several significant properties of these mappings in relation to fixed point theory in CAT(0) spaces. Specifically, we establish that these mappings are Lipschitz continuous, satisfying the demiclosedness-type property, and possessing a closed convex fixed point set. Furthermore, we show that the fixed points of the mappings can be effectively approximated using an iterative scheme for fixed points of nonexpansive mappings. The results in this work contribute to a deeper understanding of strictly pseudocontractive mappings and their applicability in the context of fixed point theory in metric spaces. © 2024, SINUS Association. All rights reserved.

Keywords

enriched nonexpansive, strictly pseudocontractive