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Best Proximity Point Theorems for Two Weak Cyclic Contractions on Metric-Like Spaces

1
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
2
Institute for Computational and Modeling Science, National Tsing Hua University, 521 Nan-Dah Road, Hsinchu City 30013, Taiwan
*
Authors to whom correspondence should be addressed.
Mathematics 2019, 7(4), 349; https://doi.org/10.3390/math7040349
Received: 3 April 2019 / Revised: 10 April 2019 / Accepted: 11 April 2019 / Published: 14 April 2019
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PDF [246 KB, uploaded 14 April 2019]

Abstract

In this paper, we establish two best proximity point theorems in the setting of metric-like spaces that are based on cyclic contraction: Meir–Keeler–Kannan type cyclic contractions and a generalized Ćirić type cyclic φ -contraction via the MT -function. We express some examples to indicate the validity of the presented results. Our results unify and generalize a number of best proximity point results on the topic in the corresponding recent literature. View Full-Text
Keywords: best proximity point theorem; cyclic Meir–Keeler–Kannan type contraction; generalized MT-Ćirić -function type cyclic φ-contraction; metric-like space best proximity point theorem; cyclic Meir–Keeler–Kannan type contraction; generalized MT-Ćirić -function type cyclic φ-contraction; metric-like space
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Karapınar, E.; Chen, C.-M.; Lee, C.-T. Best Proximity Point Theorems for Two Weak Cyclic Contractions on Metric-Like Spaces. Mathematics 2019, 7, 349.

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