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Liu1 Ruijuan,Liu Chunyan,Zhang Zihou 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.1
Let C be a closed bounded convex subset of a real Banach space X with 0 as its interior point and pc the Minkowski functional generated by the set C. For a nonempty set G in X and x ∈ X, g_0 ∈ G is called the generalized best approximation to x from G if p_c(g_0 − x) ≤ p_c(g − x) for all g ∈ G. 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.