Some generalizations of locally and weakly locally uniformly convex space

DOI10.1016/j.na.2011.02.025zbMath1232.46016OpenAlexW2047524184MaRDI QIDQ544154

Yong-Cai Geng, Sumit K. Garg

Publication date: 14 June 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2011.02.025

zbMATH Keywords

\(k\)-strongly convex space\(k\)-very convex spacealmost locally uniformly rotund spacestrongly Chebyshev setstrongly convex spacevery convex spaceweakly almost locally uniformly rotund space

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 (7)

Near convexity, near smoothness and approximative compactness of half spaces in Banach spaces ⋮ Some equivalent conditions of proximinality in nonreflexive Banach spaces ⋮ Convexities and existence of the farthest point ⋮ Convexity and proximinality in Banach space ⋮ Continuity of generalized metric projections in Banach spaces ⋮ Geometric properties and continuity of the pre-duality mapping in Banach space ⋮ Controllability for a class of time-varying controlled switching impulsive systems with time delays

Cites Work

• Convexities and approximative compactness and continuity of metric projection in Banach spaces
• On the k-uniform rotund and the fully convex Banach spaces
• Geometrical properties determined by the higher duals of a Banach space
• Geometrical implications of upper semi-continuity of the duality mapping on a Banach space
• On very rotund Banach space
• Some generalizations of locally uniform rotundity
• \(k\)-super-strongly convex and \(k\)-super-strongly smooth Banach spaces
• Proximinality in Banach spaces
• A Generalization of Uniformly Rotund Banach Spaces
• Some properties related to nested sequences of balls in Banach spaces
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