Nonlinear Sherman-type inequalities

DOI10.1515/anona-2018-0098zbMath1431.26010OpenAlexW2889748387MaRDI QIDQ2311821

Marek Niezgoda

Publication date: 4 July 2019

Published in: Advances in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/anona-2018-0098

zbMATH Keywords

convex functiongradientmajorizationdirectional derivativeSherman inequalityHLPK inequalityconvex-concave map

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Convexity of real functions of several variables, generalizations (26B25) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (11)

On generalized Csiszár (f,g)-divergence with an application for p-majorization ⋮ Sherman's inequality and its converse for strongly convex functions with applications to generalized f-divergences ⋮ A Jensen-Sherman type inequality with a control map for \(G\)-invariant convex functions ⋮ New versions of uniformly convex functions via quadratic complete homogeneous symmetric polynomials ⋮ Sherman's functional, its properties with applications for f-divergence measure ⋮ The Hardy-Littlewood-Pólya inequality of majorization in the context of \(\omega\)-\(\mathbf{m}\)-star-convex functions ⋮ Von Neumann-Davis type theorems for HLPK and Sherman functionals on Eaton triples ⋮ More accurate majorization inequalities obtained via superquadraticity and convexity with application to entropies ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Sherman's operator inequality

Cites Work

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• Vector joint majorization and generalization of Csiszár-Körner's inequality for \(f\)-divergence
• Generalizations of Sherman's inequality by Lidstone's interpolating polynomial
• An inequality for convex functions involving G-majorization
• Reflection groups, generalized Schur functions, and the geometry of majorization
• Generalizations of Sherman's inequality
• On Sherman method to deriving inequalities for some classes of functions related to convexity
• Remarks on Sherman like inequalities for (α,β)-convex functions
• On a Theorem of Hardy, Littlewood, Polya, and Blackwell
• Inequalities: theory of majorization and its applications

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