Optimal pair of fixed points for a new class of noncyclic mappings under a $ (\varphi, \mathcal{R}^t) $-enriched contraction condition-Reference-Cited by-同舟云学术

Optimal pair of fixed points for a new class of noncyclic mappings under a $ (\varphi, \mathcal{R}^t) $-enriched contraction condition

Published:2024 Issue:4 Volume:32 Page:2251-2266
ISSN:2688-1594
Container-title:Electronic Research Archive
language:
Short-container-title:era

Author:

Safari-Hafshejani A.¹,Gabeleh M.²,De la Sen M.³

Affiliation:

1. Department of Pure Mathematics, Payame Noor University (PNU), Tehran, Iran

2. Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran

3. Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, Leioa 48940, Spain

Abstract

<abstract><p>In the present study, we commenced by presenting a new class of maps, termed noncyclic $ (\varphi, \mathcal{R}^t) $-enriched quasi-contractions within metric spaces equipped with a transitive relation $ \mathcal{R}^t $. Subsequently, we identified the conditions for the existence of an optimal pair of fixed points pertaining to these mappings, thereby extending and refining a selection of contemporary findings documented in some articles. Specifically, our analysis will encompass the outcomes pertinent to reflexive and strictly convex Banach spaces.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference29 articles.

1. R. Espínola, M. Gabeleh, On the structure of minimal sets of relatively nonexpansive mappings, Numer. Funct. Anal. Optim., 34 (2013), 845–860. https://doi.org/10.1080/01630563.2013.763824

2. M. Gabeleh, Convergence of Picard's iteration using projection algorithm for noncyclic contractions, Indagationes Math., 30 (2019), 227–239. https://doi.org/10.1016/j.indag.2018.11.001

3. A. Abkar, M. Gabeleh, Global optimal solutions of noncyclic mappings in metric space, J. Optim. Theory Appl., 153 (2012), 298–305. https://doi.org/10.1007/s10957-011-9966-4

4. L. B. Ćirić, A generalization of Banach's contraction principle, Proc. Amer.Math. Soc., 45 (1974), 267–273. https://doi.org/10.1090/s0002-9939-1974-0356011-2

5. A. Fernández-León, M. Gabeleh, Best proximity pair theorems for noncyclic mappings in Banach and metric spaces, Fixed Point Theory, 17 (2016), 63–84.