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

Yahya Almalki; Fahim Ud Din; Muhammad Din; Muhammad Usman Ali; Noor Jan; Yahya Almalki; Fahim Ud Din; Muhammad Din; Muhammad Usman Ali; Noor Jan

doi:10.3934/math.20221105

AIMS Mathematics

2022, Volume 7, Issue 11: 20199-20212. doi: 10.3934/math.20221105

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

1.
Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
2.
Abdus Salam School of Mathematical Sciences, Lahore, Pakistan
3.
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan
4.
Afghan Institute of Sciences, Kabul, Afghanistan

Received: 11 May 2022 Revised: 31 August 2022 Accepted: 31 August 2022 Published: 15 September 2022
MSC : 47H10, 54H25

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.
- binary relation,
- Perov-fixed point,
- vector-valued metric space
Citation: Yahya Almalki, Fahim Ud Din, Muhammad Din, Muhammad Usman Ali, Noor Jan. Perov-fixed point theorems on a metric space equipped with ordered theoretic relation[J]. AIMS Mathematics, 2022, 7(11): 20199-20212. doi: 10.3934/math.20221105

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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.

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