Strong convexity and separation theorems

DOI10.1007/s00010-015-0360-4zbMath1342.26029OpenAlexW2555251892WikidataQ59473067 ScholiaQ59473067MaRDI QIDQ264150

Nelson Merentes, Kazimierz Nikodem

Publication date: 6 April 2016

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-015-0360-4

zbMATH Keywords

Hyers-Ulam stability\(c\)-quadratic-affine functionsapproximately concave functionsseparation theoremsstrongly convex functions

Mathematics Subject Classification ID

Functional inequalities, including subadditivity, convexity, etc. (39B62) Convexity of real functions in one variable, generalizations (26A51)

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On a generalization of sandwich type theorems ⋮ On slack $2$-geodesic convex set and geodesic $E$-pseudoconvex function with application ⋮ Separation by Jensen and affine stochastic processes ⋮ Functions generating \((m,M,\Psi)\)-Schur-convex sums ⋮ Jensen's and Hermite-Hadamard's type inequalities for lower and strongly convex functions on normed spaces ⋮ Separation by strongly h-convex functions ⋮ Characterization of inner product spaces and quadratic functions by some classes of functions ⋮ Strong \(h\)-convexity and separation theorems ⋮ Remarks on \((F, t)\)-convex functions ⋮ Lagrange’s theorem, convex functions and Gauss map

Cites Work

• Characterizations of inner product spaces by strongly convex functions
• Remarks on strongly convex functions
• On the abstract Hahn-Banach theorem due to Rodé
• A sandwich theorem and Hyers-Ulam stability of affine functions
• Separation via quadratic functions
• Strongly convex analysis
• A selection theorem of Helly type and its applications
• Abstract separation theorems of Rodé type and their applications
• On Strongly Convex Functions and Related Classes of Functions
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