Completeness of metric spaces and existence of best proximity points

Arshad Ali Khan; Basit Ali; Talat Nazir; Manuel de la Sen; Arshad Ali Khan; Basit Ali; Talat Nazir; Manuel de la Sen

doi:10.3934/math.2022408

AIMS Mathematics

2022, Volume 7, Issue 5: 7318-7336. doi: 10.3934/math.2022408

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Research article

Completeness of metric spaces and existence of best proximity points

1.
Department of Mathematics, School of Science, University of Management and Technology, C-II, Johar Town, Lahore 54770, Pakistan
2.
Department of Mathematical Sciences, University of South Africa, Florida 0003, South Africa
3.
Institute of Research and Development of Processes, University of the Basque Country, 48940, Leioa, Bizkaia, Spain

Received: 24 October 2021 Revised: 24 January 2022 Accepted: 24 January 2022 Published: 10 February 2022
MSC : 47H04, 47H07, 47H09, 90C26

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.
- Suzuki-type,
- best proximity point,
- proximal contractions,
- $ \alpha _{p} $-proximal admissible,
- partial order
Citation: Arshad Ali Khan, Basit Ali, Talat Nazir, Manuel de la Sen. Completeness of metric spaces and existence of best proximity points[J]. AIMS Mathematics, 2022, 7(5): 7318-7336. doi: 10.3934/math.2022408

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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.

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