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Research Article | Open Access

Completeness of metric spaces and existence of best proximity points

Arshad Ali Khan1, Basit Ali1( ), Talat Nazir2, Manuel de la Sen3
Department of Mathematics, School of Science, University of Management and Technology, C-II, Johar Town, Lahore 54770, Pakistan
Department of Mathematical Sciences, University of South Africa, Florida 0003, South Africa
Institute of Research and Development of Processes, University of the Basque Country, 48940, Leioa, Bizkaia, Spain
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Abstract

In this paper, we discuss the existence of best proximity points of new generalized proximal contractions of metric spaces. Moreover, we obtain a completeness characterization of underlying metric space via the best proximity points. Some new best proximity point theorems have been derived as consequences of main results in (partially ordered) metric spaces.

Keywords

Suzuki-typebest proximity pointproximal contractionsαp-proximal admissiblepartial order
CLC number: 47H04, 47H07, 47H09, 90C26

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 7318-7336
DOI: 10.3934/math.2022408

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Cite this article:
Khan AA, Ali B, Nazir T, et al. Completeness of metric spaces and existence of best proximity points. AIMS Mathematics, 2022, 7(5): 7318-7336. https://doi.org/10.3934/math.2022408

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Received: 24 October 2021
Revised: 24 January 2022
Accepted: 24 January 2022
Published: 15 May 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)