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Research Article | Open Access

Perov-fixed point theorems on a metric space equipped with ordered theoretic relation

Yahya Almalki1, Fahim Ud Din2, Muhammad Din2, Muhammad Usman Ali3( ), Noor Jan4( )
Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
Abdus Salam School of Mathematical Sciences, Lahore, Pakistan
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan
Afghan Institute of Sciences, Kabul, Afghanistan
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Abstract

In this paper, we introduce a few new generalizations of the classical Perov-fixed point theorem for single-valued and multi-valued mappings in a complete generalized metric space endowed with a binary relation. We have furnished our work with examples to show that several metrical-fixed point theorems can be obtained from an arbitrary binary relation.

Keywords

binary relationPerov-fixed pointvector-valued metric space
CLC number: 47H10, 54H25

References

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AIMS Mathematics
Volume 7 Issue 11,
November 2022
Pages 20199-20212
DOI: 10.3934/math.20221105

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Cite this article:
Almalki Y, Din FU, Din M, et al. Perov-fixed point theorems on a metric space equipped with ordered theoretic relation. AIMS Mathematics, 2022, 7(11): 20199-20212. https://doi.org/10.3934/math.20221105

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Received: 11 May 2022
Revised: 31 August 2022
Accepted: 31 August 2022
Published: 15 November 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)