MULTIPLED BEST PROXIMITY POINTS FOR GENERALIZED CYCLIC ω-CONTRACTIONS

MULTIPLED BEST PROXIMITY POINTS

Abstract

Non-self mappings from $A$ to $B$ do not necessarily have fixed points. However, when $A$ and $B$ are subsets of a distance type space, it is of interest to find elements as close as possible to their image. These elements are called best proximity points. In this paper, we prove the existence of multipled best proximity points of generalized cyclic contractions in metric spaces. The contractive condition is quite encompassing, generalizing, unifying and providing an erratum to existing related works in literature. An example is also given to illustrate the result.