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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 경남대학교 기초과학연구소 Nonlinear Functional Analysis and Applications Nonlinear Functional Analysis and Applications Vol.24 No.1
- 발행연도
- 2019.1
- 수록면
- 175 - 183 (9page)
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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.
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참고문헌 (10)
참고문헌 신청
F. S. De Blasi / 1998 / On a generalized best approximation problem / J. of Appro. Theory 94:54~72
X. N. Fang / 2001 / Convexity and the continuity of metric projections / Math. Applicata 14(1):47~51
O. P. Ferreira / 2012 / Generalized projections onto convex sets / J. of Global Optim 52(4):831~842
C. Li / 2000 / On well-posed generalized best approximation problems / J. of Appro. Theory 107:96~108
X.F. Luo / 2013 / The representation and continuity of a generalized metric projection onto a closed hyperplane in Banach Space / Abstract and Appl. Anal. :504076
X. N. Fang / 2001 / Convexity and the continuity of metric projections / Math. Applicata 14(1):47~51
O. P. Ferreira / 2012 / Generalized projections onto convex sets / J. of Global Optim 52(4):831~842
C. Li / 2000 / On well-posed generalized best approximation problems / J. of Appro. Theory 107:96~108
X.F. Luo / 2013 / The representation and continuity of a generalized metric projection onto a closed hyperplane in Banach Space / Abstract and Appl. Anal. :504076
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