A note in approximative compactness and midpoint locally \(k\)-uniform rotundity in Banach spaces

DOI10.1016/S0252-9602(18)30771-9zbMath1399.46018OpenAlexW2789396083MaRDI QIDQ1637049

Yu Zhou, Chun Yan Liu, Zi Hou Zhang

Publication date: 7 June 2018

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0252-9602(18)30771-9

zbMATH Keywords

approximative compactness\(k\)-Chebyshev setapproximatively weak compactness\(k\)-strict rotunditymidpoint locally \(k\)-uniform rotundityweak midpoint locally \(k\)-uniform rotundity

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)

Related Items (3)

Some equivalent conditions of proximinality in nonreflexive Banach spaces ⋮ Some metric and topological properties of nearly strongly and nearly very convex spaces ⋮ On geometric and best approximation properties of \(k\)-UR and its generalizations

Cites Work

• Some examples concerning proximinality in Banach spaces
• Convexity and proximinality in Banach space
• Convexities and approximative compactness and continuity of metric projection in Banach spaces
• On the k-uniform rotund and the fully convex Banach spaces
• Approximate compactness in Orlicz spaces
• Approximative compactness and full rotundity in Musielak--Orlicz spaces and Lorentz--Orlicz spaces
• On the Lk-UR and L-kR spaces
• An Introduction to Banach Space Theory
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