The existence of best proximity points for cyclic quasi-φ-contractions in metric spaces

Abstract

In this paper, we introduce the notion of cyclic quasi-φ-contraction. We prove the existence and uniqueness of best proximity points for this class of mappings on a metric space endowed with ultrametric and UC properties. Also, iterative algorithms are furnished to determine such best proximity points. As a result, we establish a fixed point result and a common fixed point theorem. Our results, while generalizing a few existing results in the literature, unify and integrate them.