Common Best Proximity Points and Completeness of ℱ−Metric Spaces

Mi Zhou, Naeem Saleem, Basit Ali (), Misha Mohsin and Antonio Francisco Roldán López de Hierro ()
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Mi Zhou: School of Science and Technology, Sanya University, Sanya 572000, China
Naeem Saleem: Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan
Basit Ali: Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan
Misha Mohsin: Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan
Antonio Francisco Roldán López de Hierro: Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain

Mathematics, 2023, vol. 11, issue 2, 1-21

Abstract: In this paper, we introduce three classes of proximal contractions that are called the proximally λ − ψ − dominated contractions, generalized η β γ − proximal contractions and Berinde-type weak proximal contractions, and obtain common best proximity points for these proximal contractions in the setting of F − metric spaces. Further, we obtain the best proximity point result for generalized α − φ − proximal contractions in F − metric spaces. As an application, fixed point and coincidence point results for these contractions are obtained. Some examples are provided to support the validity of our main results. Moreover, we obtain a completeness characterization of the F − metric spaces via best proximity points.

Keywords: common best proximity point; proximally λ − ψ −dominated contraction; generalized η β γ − proximal contraction; Berinde-type weak proximal contraction; generalized α − φ −proximal contraction; ℱ−metric spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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