On continuity of metric projections

DOI10.1016/0021-9045(80)90110-0zbMath0514.41034OpenAlexW1994594876MaRDI QIDQ1051182

Joseph M. Lambert, Frank Deutsch

Publication date: 1980

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(80)90110-0

zbMATH Keywords

metric projectionnearest pointscompactly locally uniformly rotund normed vector space

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (11)

Metric spaces with nice closed balls and distance functions for closed sets ⋮ Connectedness and other geometric properties of suns and Chebyshev sets ⋮ On modular approximants in sequential convergence spaces ⋮ Centers and Nearest Points of Sets ⋮ Weakly compactly LUR Banach spaces ⋮ Approximating properties of metric and generalized metric projections in uniformly convex and uniformly smooth Banach spaces ⋮ Chebyshev unions of planes, and their approximative and geometric properties ⋮ On the norms of metric projections ⋮ Unnamed Item ⋮ On a generic optimization theorem of Petar Kenderov ⋮ Metric projection bound an the Lipschitz constant of the radial retraction

Cites Work

• Radial continuity of set-valued metric projections
• On some geometric properties of suns
• Chebyshev sets and approximately convex sets
• Smoothness of approximation
• Charakterisierung bester Approximationen in normierten Vektorräumen
• Approximative compactness and continuity of metric projections: Corrigendum
• APPROXIMATIVE PROPERTIES OF SETS IN NORMED LINEAR SPACES
• Continuous Metric Projections
• Two renorming constructions related to a question of Anselone
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