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

Nesrin Manav Tatar () and Ravi P. Agarwal
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Nesrin Manav Tatar: Department of Mathematics, Erzincan Binali Yildirim University, Erzincan 24002, Turkey
Ravi P. Agarwal: Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, USA

Mathematics, 2023, vol. 11, issue 21, 1-15

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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