A discussion on the existence of best proximity points that belong to the zero set

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Authors

Karapınar, Erdal
Abbas, Mujahid
Farooq, Sadia

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MDPI

Abstract

In this paper, we investigate the existence of best proximity points that belong to the zero set for the αp-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.

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Keywords

M-metric space, Proximal αp-admissible, Ap-admissible weak (F, ϕ)-proximal contraction, G−proximal graphic contraction, ϕ-best proximity point

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Citation

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. https://doi.org/10.3390/axioms9010019.