# Coincidence best proximity points for geraghty type proximal cyclic contractions

Volume 18, Issue 1, pp 98--114 Publication Date: January 10, 2018       Article History
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### Authors

Somayya Komal - Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand Azhar Hussain - Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan Nazra Sultana - Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan Poom Kumam - Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand

### Abstract

In this paper, we study the notions of generalized Geraghty proximal cyclic contractions for non-self mapping and obtain coincidence best proximity point theorems in the framework of complete metric spaces. Some examples are given to show the validity of our results. Our results extended and unify many existing results in the literature.

### Keywords

• $\alpha$-Geraghty proximal contraction of first and second kind
• $\alpha$-proximal cyclic contraction
• $\alpha$-proximal admissible maps

•  55M20

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