Abstract
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.
Highlights
Introduction and PreliminariesSeveral real-world problems can be reformulated as a fixed point problem
We characterize the following sets in the setting of M-metric space
We introduce the notion of φ-best proximity point and prove the φ-best proximity point result in the setting of M-metric space
Summary
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan Department of Mathematics, Government College University, Lahore 54000, Pakistan Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Road, Pretoria 0002, South Africa These authors contributed equally to this work. Received: 13 December 2019; Accepted: 6 February 2020; Published: 11 February 2020
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