A BEST APPROXIMATION THEOREM FOR SET-VALUED MAPPINGS IN REFLEXIVE BANACH SPACES

Abstract

In this paper, we prove a best approximation theorem for set-valued mappings, in re°exive Banach spaces. From this theorem we deduce some corollaries and some fixed-point theorems. We use the method of KKM-mappings and a Ky Fan's-KKM type Theorem.