Author： Sababheh M.
Publisher： Taylor & Francis Ltd
ISSN： 0163-0563
Source： Numerical Functional Analysis and Optimization, Vol.29, Iss.9-10, 2008-09, pp. : 1166-1170
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Abstract
Let X be a Banach space and E be a closed bounded subset of X. For x ∈ X, we define D(x, E) = sup{‖ x - e‖:e ∈ E}. The set E is said to be remotal (in X) if, for every x ∈ X, there exists e ∈ E such that D(x, E) = ‖x - e‖. The object of this paper is to characterize those reflexive Banach spaces in which every closed bounded convex set is remotal. Such a result enabled us to produce a convex closed and bounded set in a uniformly convex Banach space that is not remotal. Further, we characterize Banach spaces in which every bounded closed set is remotal.
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