Abstract

LetX be a Banach space, andE X be a non-empty closed bounded subset ofX: The setE is called proximinal inX if for allx2 X there is somee2 E such thatkx ek = inffkx yk : y2 Eg: E is called remotal in X if for all x 2 X, there exists e 2 E such thatkx ek = supfkx yk : y2 Eg: The concept of strong proximinality is well known by now in the literature, and many results were obtained. In this paper we introduce the concept of strong remotality of sets. Many results are presented.

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