Farthest points and strong convexity of sets

DOI10.1134/S0001434610030065zbMath1211.46011MaRDI QIDQ1957057

Grigorii E. Ivanov

Publication date: 24 September 2010

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Hausdorff metricBanach spaceoptimization problemMinkowski sumFréchet differentiable normfarthest pointsantisunmetric antiprojectionstrong convexity of a set

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 (10)

Estimates of the Chebyshev radius in terms of the MAX-metric function and the MAX-projection operator ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Monotonicity and the dominated farthest points problem in Banach lattice ⋮ Unnamed Item ⋮ Solarity of Chebyshev sets in dual spaces and uniquely remotal sets ⋮ Unnamed Item ⋮ The attainment set of the $\varphi$-envelope and genericity properties ⋮ Solarity of sets in max-approximation problems

Cites Work

• Geometry of Banach spaces. Selected topics
• Proximality and Chebyshev sets
• Farthest points in reflexive locally uniformly rotund Banach spaces
• Farthest points of sets in uniformly convex Banach spaces
• Metric projections and the differentiability of distance functions
• APPROXIMATIVE PROPERTIES OF SETS IN NORMED LINEAR SPACES
• Weakly convex and proximally smooth sets in Banach spaces
• On farthest points of sets
• Sets with external Chebyshev layer
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