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Volume 11
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10.3390/math11214455
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Article

Best Approximation of Fixed-Point Results for Branciari Contraction of Integral Type on Generalized Modular Metric Space

by
Nesrin Manav Tatar
1,* and
Ravi P. Agarwal
2
1
Department of Mathematics, Erzincan Binali Yildirim University, Erzincan 24002, Turkey
2
Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, USA
*
Author to whom correspondence should be addressed.
Mathematics 2023, 11(21), 4455; https://doi.org/10.3390/math11214455
Submission received: 23 September 2023 / Revised: 24 October 2023 / Accepted: 26 October 2023 / Published: 27 October 2023
(This article belongs to the Special Issue Fixed Point Theory and Its Applications in Nonlinear Analysis and Optimization)
Versions Notes

Abstract

In the realm of generalized modular metric spaces, we substantiate the validity of fixed-point theorems with Branciari contractions. This paper expands and broadens the original theorems in this context. Subsequently, by building upon this foundation, we explore various integral contractions to identify and characterize fixed points within this context. To highlight the practical implications of our work, we introduce the concept of the best proximity pair, thereby culminating in the best approximation theorem. We apply this theoretical construct to a specific example—one that is guided by the best approximation method described in prior research.
Keywords: fixed-point theorem; generalized metric space; modular metric space; integral-type contraction; best approximation fixed-point theorem; generalized metric space; modular metric space; integral-type contraction; best approximation

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MDPI and ACS Style

Manav Tatar, N.; Agarwal, R.P. Best Approximation of Fixed-Point Results for Branciari Contraction of Integral Type on Generalized Modular Metric Space. Mathematics 2023, 11, 4455. https://doi.org/10.3390/math11214455

AMA Style

Manav Tatar N, Agarwal RP. Best Approximation of Fixed-Point Results for Branciari Contraction of Integral Type on Generalized Modular Metric Space. Mathematics. 2023; 11(21):4455. https://doi.org/10.3390/math11214455

Chicago/Turabian Style

Manav Tatar, Nesrin, and Ravi P. Agarwal. 2023. "Best Approximation of Fixed-Point Results for Branciari Contraction of Integral Type on Generalized Modular Metric Space" Mathematics 11, no. 21: 4455. https://doi.org/10.3390/math11214455

APA Style

Manav Tatar, N., & Agarwal, R. P. (2023). Best Approximation of Fixed-Point Results for Branciari Contraction of Integral Type on Generalized Modular Metric Space. Mathematics, 11(21), 4455. https://doi.org/10.3390/math11214455

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