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Best proximity point results for Suzuki-Edelstein proximal contractions via auxiliary functions

Hussain Azhar (Department of Mathematics, University of Sargodha, Sargodha, Pakistan)
Iqbal Muhammad Qamar (Department of Mathematics, University of Sargodha, Sargodha, Pakistan)
Hussain Nawab (Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia)

In this paper we study the notion of modified Suzuki-Edelstein proximal contraction under some auxiliary functions for non-self mappings and obtain best proximity point theorems in the setting of complete metric spaces. As applications, we derive best proximity point and fixed point results for such contraction mappings in partially ordered metric spaces. Some examples are given to show the validity of our results. Our results extend and unify many existing results in the literature.

Keywords: Best proximity points, Suzuki contraction, coupled fixed point theorem