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

A. Safari-Hafshejani; M. Gabeleh; M. De la Sen; A. Safari-Hafshejani; M. Gabeleh; M. De la Sen

doi:10.3934/era.2024102

Electronic Research Archive

2024, Volume 32, Issue 4: 2251-2266. doi: 10.3934/era.2024102

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

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

Received: 28 December 2023 Revised: 11 February 2024 Accepted: 08 March 2024 Published: 21 March 2024

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.
- optimal pair of fixed points,
- noncyclic $ (\varphi, \mathcal{R}^t) $-enriched quasi-contraction,
- metric space,
- transitive relation,
- reflexive Banach space
Citation: A. Safari-Hafshejani, M. Gabeleh, M. De la Sen. Optimal pair of fixed points for a new class of noncyclic mappings under a $ (\varphi, \mathcal{R}^t) $-enriched contraction condition[J]. Electronic Research Archive, 2024, 32(4): 2251-2266. doi: 10.3934/era.2024102

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Abstract

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.

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