Best proximity points for tricyclic contractions

Abstract

Consider a self mapping T defined on the union of three subsets A,B andC of a metric space, T is to be called a tricyclic mapping if it satisfies T (A)⊆B, T (B)⊆C and T (C)⊆A. In this work we shall give an existence theorem of a best proximity point for tricyclic contractions in reflexive Banach spaces. The concept of tricyclic contractions is firstly introduced in this article.