THE REPRESENTATION AND CONTINUITY OF A GENERALIZED METRIC PROJECTION ONTO HALF-SPACES IN BANACH SPACES

Abstract

In this paper, we will give a distance formula under p_C from a point to a half-space K_{x^∗_0, c} = {x ∈ X : x^∗_0(x) ≤ c} in Banach space and investigate the continuity of this generalized metric projection, extending corresponding results for the case of norm.