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Admissible Hybrid Z-Contractions in b-Metric Spaces
Open AccessArticle

A Discussion on the Existence of Best Proximity Points That Belong to the Zero Set

by Erdal Karapınar 1,2,*,†, Mujahid Abbas 3,4,*,† and Sadia Farooq 5,†
1
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
2
Department of Mathematics, Çankaya University, Etimesgut 06790, Ankara, Turkey
3
Department of Mathematics, Government College University, Lahore 54000, Pakistan
4
Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Road, Pretoria 0002, South Africa
5
Department of Mathematics, University of Management and Technology, Lahore 54782, Pakistan
*
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Axioms 2020, 9(1), 19; https://doi.org/10.3390/axioms9010019
Received: 13 December 2019 / Revised: 5 February 2020 / Accepted: 6 February 2020 / Published: 11 February 2020
(This article belongs to the Special Issue Nonlinear Analysis and Optimization with Applications)
In this paper, we investigate the existence of best proximity points that belong to the zero set for the α p -admissible weak ( F , φ ) -proximal contraction in the setting of M-metric spaces. For this purpose, we establish φ -best proximity point results for such mappings in the setting of a complete M-metric space. Some examples are also presented to support the concepts and results proved herein. Our results extend, improve and generalize several comparable results on the topic in the related literature.
Keywords: m-metric space; proximal αp-admissible; αp-admissible weak (F,φ)-proximal contraction; G-proximal graphic contraction; φ-best proximity point m-metric space; proximal αp-admissible; αp-admissible weak (F,φ)-proximal contraction; G-proximal graphic contraction; φ-best proximity point
MDPI and ACS Style

Karapınar, E.; Abbas, M.; Farooq, S. A Discussion on the Existence of Best Proximity Points That Belong to the Zero Set. Axioms 2020, 9, 19.

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