Metric Projection Operator and Continuity of the Set-Valued Metric Generalized Inverse in Banach Spaces

In this paper, continuous homogeneous selection and continuity for the set-valued metric generalized inverses in 3-strictly convex spaces are investigated by continuity of metric projection. The results are an answer to the problem posed by Nashed and Votruba. Moreover, authors prove that there exists a proximinal hyperplane such that is continuous and is not approximative compact.

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