Fixed point theorems for enriched Kannan mappings in CAT(0) spaces

Journal article

Authors/Editors

Strategic Research Themes

Modeling Design and Optimization (Computational Science and Engineering)

Publication Details

Author list: Inuwa A.Y.; Kumam P.; Chaipunya P.; Salisu S.

Publisher: Springer Open

Publication year: 2023

Volume number: 2023

Issue number: 1

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85174227176&doi=10.1186%2fs13663-023-00750-1&partnerID=40&md5=e4e01c3530372835e589eae5092886c9

Languages: English-Great Britain (EN-GB)

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Abstract

We present enriched Kannan and enriched Bianchini mappings in the framework of unique geodesic spaces. For such mappings, we establish the existence and uniqueness of a fixed point in the setting of CAT(0) spaces and show that an appropriate Krasnoselskij scheme converges with certain rate to the fixed point. We proved some inclusion relations between enriched Kannan mapping and some applicable mappings such as strongly demicontractive mapping. Finally, we give an example in a nonlinear CAT(0) space and perform numerical experiments to support the theoretical results. ฉ 2023, Springer Nature Switzerland AG.

Keywords

Enriched Bianchini mapping, Enriched Kannan Mapping, Kransnoselskij iteration, Strongly demicontractive mapping