Strong uniqueness of the restricted Chebyshev center with respect to an RS-set in a Banach space

Abstract

Let G be a strict RS -set ( resp . an RS -set) in X and let F be a bounded ( resp. totally bounded) subset of X satisfying r G ( F ) > r X ( F ) , where r G ( F ) is the restricted Chebyshev radius of F with respect to G . It is shown that the restricted Chebyshev center of F with respect to G is strongly unique in the case when X is a real Banach space, and that, under some additional convexity assumptions, the restricted Chebyshev center of F with respect to G is strongly unique of order α ⩾ 2 in the case when X is a complex Banach space.