Some new estimates of the `Jensen gap'

DOI10.1186/s13660-016-0985-4zbMath1336.26019OpenAlexW2259314895WikidataQ59480331 ScholiaQ59480331MaRDI QIDQ5964633

Shoshana Abramovich, Lars-Erik Persson

Publication date: 29 February 2016

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-016-0985-4

zbMATH Keywords

convex functionTaylor expansionJensen inequality\(\gamma\)-superconvex functionssuperquadratic functions

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 (8)

Bounds on the Jensen Gap, and Implications for Mean-Concentrated Distributions ⋮ From integral estimates of functions to uniform and locally averaged ones ⋮ Convexity Variants and Fejer Inequalities with General Weight ⋮ Fejér and Hermite-Hadamard type inequalities for \(N\)-quasiconvex functions ⋮ Some new Hermite-Hadamard and Fejer type inequalities without convexity/concavity ⋮ Hermite-Hadamard, Fejer and Sherman type inequalities for generalizations of superquadratic and convex functions ⋮ Extensions and refinements of Fejer and Hermite-Hadamard type inequalities ⋮ Sharpening Jensen's Inequality

Cites Work

• Unnamed Item
• Refinement of Hardy's inequalities via superquadratic and subquadratic functions
• Some new scales of refined Hardy type inequalities via functions related to superquadracity
• On γ-quasiconvexity, superquadracity and two-sided reversed Jensen type inequalities
• Some new scales of refined Jensen and Hardy type inequalities
• On a Lower Bound for the Jensen Inequality
• Some New Refined Hardy Type Inequalities with Breaking Points p = 2 or p = 3

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