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Research Article | Open Access

Paired contractive mappings and fixed point results

Deep Chand1( ), Yumnam Rohen1,2
Department of Mathematics, National Institute of Technoogy Manipur, Langol-795004, Imphal, Manipur, India
Department of Mathematics, Manipur University, Canchipur, Imphal-795003, Manipur, India
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Abstract

In this study, we explored a novel type of contraction, known as paired contraction (PC), to establish fixed points in metric spaces. It has been demonstrated that mappings possessing the PC property are continuous. We have also provided proofs for the existence of fixed points for such mappings with the classical Banach fixed point theorem emerging as a corollary. Furthermore, we presented examples of mappings that do not satisfy the standard contraction condition, but do exhibit the PC property.

Keywords

metric spaceBanach contractionpaired contraction (PC)fixed point
CLC number: 47H09, 47H10

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AIMS Mathematics
Volume 9 Issue 1,
January 2024
Pages 1959-1968
DOI: 10.3934/math.2024097

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Cite this article:
Chand D, Rohen Y. Paired contractive mappings and fixed point results. AIMS Mathematics, 2024, 9(1): 1959-1968. https://doi.org/10.3934/math.2024097

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Received: 02 November 2023
Revised: 01 December 2023
Accepted: 08 December 2023
Published: 15 January 2024
©2024 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)