Extremal approximately convex functions and estimating the size of convex hulls

DOI10.1006/aima.1999.1836zbMath0949.26003arXivmath/9807107OpenAlexW2012800560MaRDI QIDQ1969013

James W. Roberts, Ralph Howard, Stephen Dilworth

Publication date: 3 December 2000

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9807107

zbMATH Keywords

convex hullapproximately convex functionapproximately convex set

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Inequalities and extremum problems involving convexity in convex geometry (52A40) Convexity of real functions of several variables, generalizations (26B25) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Approximation by convex sets (52A27)

Related Items (8)

On approximately convex and affine functions ⋮ Approximate convexity and submonotonicity. ⋮ On approximately monotone and approximately Hölder functions ⋮ Convexity of sets in metric abelian groups ⋮ A general theory of almost convex functions ⋮ Regularity theory for \(L^n\)-viscosity solutions to fully nonlinear elliptic equations with asymptotical approximate convexity ⋮ Extremal approximately convex functions and the best constants in a theorem of Hyers and Ulam. ⋮ On approximately convex functions

Cites Work

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• Almost convex sets and best approximation
• On Approximately Convex Functions
• A Generalization of a Theorem of Fenchel
• Approximately Convex Functions
• Remarks on the stability of functional equations

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