Abstract
In this paper, continuity of the set-valued metric generalized inverse T∂ in approximatively compact Banach spaces is investigated by means of the methods of geometry of Banach spaces. Necessary and sufficient conditions for upper semicontinuity (continuity) for the set-valued metric generalized inverses T∂ are given. Moreover, authors also prove that if X is a nearly dentable space and H is a hyperplane of X, then H is approximatively compact iff PH(x) is compact for any x∈X.
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