Common Best Proximity Points for Cyclic φ-Contraction Maps

Abstract

The purpose of this paper is to introduce new types of contraction condition for a pair of maps $(S,T)$ in metric spaces. We give convergence and existence results of best proximity points of such maps in the setting of uniformly convex Banach spaces. Moreover, we obtain existence theorems of best proximity points for such contraction pairs in reflexive Banach spaces. Our results generalize, extend and improve results on the topic in the literature.