Convexities and approximative compactness and continuity of metric projection in Banach spaces

DOI10.1016/j.jat.2009.01.003zbMath1190.46018OpenAlexW2024737131MaRDI QIDQ1048990

Zhong-Rui Shi, Zi Hou Zhang

Publication date: 8 January 2010

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

Full work available at URL: https://doi.org/10.1016/j.jat.2009.01.003

zbMATH Keywords

set-valued mapsChebyshev setsmetric projectionupper semi-continuityapproximative compactnessgeometry of Banach spacesproximinal sets

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

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Cites Work

• Convergence of best approximations in a smooth Banach space
• Approximative compactness and continuity of metric projector in Banach spaces and applications
• Parametric approximation
• Geometrical properties determined by the higher duals of a Banach space
• Convergence theorems for best approximations in a nonreflexive Banach space
• Approximative compactness and full rotundity in Musielak--Orlicz spaces and Lorentz--Orlicz spaces
• On the drop and weak drop properties for a Banach space
• Mosco Convergence and the Kadec Property
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