Relation-preserving generalized nonlinear contractions and related fixed point theorems

Faruk Sk; Faizan Ahmad Khan; Qamrul Haq Khan; Aftab Alam; Faruk Sk; Faizan Ahmad Khan; Qamrul Haq Khan; Aftab Alam

doi:10.3934/math.2022370

AIMS Mathematics

2022, Volume 7, Issue 4: 6634-6649. doi: 10.3934/math.2022370

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Research article

Relation-preserving generalized nonlinear contractions and related fixed point theorems

1.
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
2.
Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
3.
Department of Mathematics, Jamia Millia Islamia, New Delhi-110025, India

Received: 22 September 2021 Revised: 04 January 2022 Accepted: 11 January 2022 Published: 24 January 2022
MSC : 47H10, 54H25

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.
Citation: Faruk Sk, Faizan Ahmad Khan, Qamrul Haq Khan, Aftab Alam. Relation-preserving generalized nonlinear contractions and related fixed point theorems[J]. AIMS Mathematics, 2022, 7(4): 6634-6649. doi: 10.3934/math.2022370

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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.

References

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