Strong Uniqueness of a Class of Best Simultaneous Approximation From Rs-Sets in Normed Spaces

Abstract

This paper is concerned with the problem of best simultaneous approximations from RS-sets in Banach spaces X. It is shown that the best simultaneous approximations from an RS-set is strongly unique in the case when X is a real Banach space, and strongly unique of order α ≥ 2 in the case when X is a complex Banach space.