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Research Article | Open Access

Relation-preserving generalized nonlinear contractions and related fixed point theorems

Faruk Sk1, Faizan Ahmad Khan2( ), Qamrul Haq Khan1, Aftab Alam3( )
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
Department of Mathematics, Jamia Millia Islamia, New Delhi-110025, India
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Abstract

In this paper, we present some fixed point theorems for generalized nonlinear contractions involving a new pair of auxiliary functions in a metric space endowed with a locally finitely T-transitive binary relation. Our newly proved results generalize some well-known fixed point theorems existing in the literature. We also provide an example which substantiates the utility of our results.

Keywords

(ϕ, ψ)-contractionslocally finitely T-transitive binary relationsR-complete metric space
CLC number: 47H10, 54H25

References

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AIMS Mathematics
Volume 7 Issue 4,
April 2022
Pages 6634-6649
DOI: 10.3934/math.2022370

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Cite this article:
Sk F, Khan FA, Khan QH, et al. Relation-preserving generalized nonlinear contractions and related fixed point theorems. AIMS Mathematics, 2022, 7(4): 6634-6649. https://doi.org/10.3934/math.2022370

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Received: 22 September 2021
Revised: 04 January 2022
Accepted: 11 January 2022
Published: 15 April 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)