Best Proximity Point Theorems for Proximal Multivalued Mappings

Nuttawut Bunlue, Yeol Je Cho, Suthep Suantai


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.


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