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

Abstract EN

In this paper, continuous homogeneous selection and continuity for the set-valued metric generalized inverses T∂ 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 H such that PH is continuous and H is not approximative compact.