On strongly convex sets and strongly convex functions

DOI10.1007/BF02672709zbMath0983.52001MaRDI QIDQ1585388

E. S. Polovinkin

Publication date: 7 November 2000

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

zbMATH Keywords

generating functiongenerating set\(m\)-strongly convex function\(M\)-strongly convex hull\(M\)-strongly convex set\(R\)-strongly extreme pointMinkowski-Pontryagin difference

Mathematics Subject Classification ID

Axiomatic and generalized convexity (52A01) Selections in general topology (54C65) Convex functions and convex programs in convex geometry (52A41) Methods involving semicontinuity and convergence; relaxation (49J45) Convexity of real functions of several variables, generalizations (26B25) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Homotopy and topological questions for infinite-dimensional manifolds (58B05)

Related Items (4)

ENVELOPES FOR SETS AND FUNCTIONS: REGULARIZATION AND GENERALIZED CONJUGACY ⋮ Unnamed Item ⋮ Biholomorphic mappings of the disk onto strongly convex domains ⋮ Harmonic mappings onto R-convex domains

Cites Work

• On convex and strongly convex approximations of sets
• Surrogate conjugate functionals and surrogate convexity
• Strongly convex analysis
• On $\Phi $-Convexity in Extremal Problems
• On extreme points of regular convex sets
• A generalization of theorems of Carathéodory and Krein-Mil'man for strongly convex sets
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