Some remarks on contractive and existence sets
Abstract
Let X be a real or complex Banach space and let F in X be a non-empty set. F is called an existence set of best coapproximation (existence set for brevity), if for any x in X, RF(x) is not the empty set, where RF (x) = \ d ∈ F : \|d-c\| ≤ \|x-c\| for any c ∈ F \. It is clear that any existence set is a contractive subset of X. The aim of this paper is to present some conditions on F and X under which the notions of exsistence set and contractive set are equivalent.
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