STRONG UNIQUENESS OF A CLASS OF BEST SIMULTANEOUS APPROXIMATION FROM RS-SETS IN NORMED SPACES

Abstract

This paper is concerned with a class of 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 $\alpha \geq 2$ in the case when $X$ is a complex Banach space.