Paired contractive mappings and fixed point results

Deep Chand; Yumnam Rohen; Deep Chand; Yumnam Rohen

doi:10.3934/math.2024097

AIMS Mathematics

2024, Volume 9, Issue 1: 1959-1968. doi: 10.3934/math.2024097

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Research article

Paired contractive mappings and fixed point results

Deep Chand ^{1
,
,},
Yumnam Rohen ^1,2

1.
Department of Mathematics, National Institute of Technoogy Manipur, Langol-795004, Imphal, Manipur, India
2.
Department of Mathematics, Manipur University, Canchipur, Imphal-795003, Manipur, India

Received: 02 November 2023 Revised: 01 December 2023 Accepted: 08 December 2023 Published: 18 December 2023
MSC : 47H09, 47H10

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.
- metric space,
- Banach contraction,
- paired contraction (PC),
- fixed point
Citation: Deep Chand, Yumnam Rohen. Paired contractive mappings and fixed point results[J]. AIMS Mathematics, 2024, 9(1): 1959-1968. doi: 10.3934/math.2024097

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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.

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