Perturbation bounds for the metric projection of a point onto a linear manifold in reflexive strictly convex Banach spaces

In this paper, by using some recent perturbation bounds for the Moore-Penrose metric generalized inverse, we present some results on the perturbation analysis for projecting a point onto a linear manifold in reflexive strictly convex Banach spaces. The main results have two parts, part one covers consistent operator equations and part two covers the general so-called ill posed operator equations.

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 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.