Best Proximity Point Theorems for Proximal Multivalued Mappings

Abstract

In this paper, we introduce new classes of proximal multivalued contraction in a metric space and proximal multivalued nonexpansive mappings in a Banach space, and prove existence of best proximity points for both classes of mappings. In the case of proximal multivalued nonexpansive mappings,
we obtain a best proximity point theorem on starshape sets. As a consequence, we also obtain some new fixed point theorems. Moreover, some examples are given to support our main results.