How sharp is the Jensen inequality?

DOI10.1186/s13660-015-0591-xzbMath1309.26014OpenAlexW2127049502WikidataQ59403782 ScholiaQ59403782MaRDI QIDQ2262009

Danilo Costarelli, Renato Spigler

Publication date: 16 March 2015

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

Full work available at URL: https://doi.org/10.1186/s13660-015-0591-x

zbMATH Keywords

convex functionsOrlicz spacesHölder inequalityJensen inequalityCauchy-Schwarz inequalityconvex modular functionals

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Convexity of real functions in one variable, generalizations (26A51)

Related Items (17)

Extensional \textit{Elastica} in large deformation as \(\Gamma \)-limit of a discrete 1D mechanical system ⋮ Bounds for the Jensen gap in terms of power means with applications ⋮ Bounds on the Jensen Gap, and Implications for Mean-Concentrated Distributions ⋮ Convergence Results for Nonlinear Sampling Kantorovich Operators in Modular Spaces ⋮ Approximation error for neural network operators by an averaged modulus of smoothness ⋮ Approximation by multivariate max-product Kantorovich exponential sampling operators ⋮ A Quantitative Estimate for the Sampling Kantorovich Series in Terms of the Modulus of Continuity in Orlicz Spaces ⋮ Direct, inverse, and equivalence theorems for weighted Szász-Durrmeyer-Bézier operators in Orlicz spaces ⋮ Approximation results in Orlicz spaces for sequences of Kantorovich MAX-product neural network operators ⋮ Quantitative estimates for nonlinear sampling Kantorovich operators ⋮ Convergence of sampling Kantorovich operators in modular spaces with applications ⋮ About the sharpness of the Jensen inequality ⋮ Some improvements of Jensen's inequality via 4-convexity and applications ⋮ Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces ⋮ Approximation by max-product sampling Kantorovich operators with generalized kernels ⋮ Connections between the Approximation Orders of Positive Linear Operators and Their Max-Product Counterparts ⋮ On inequalities of Jensen-Ostrowski type

Uses Software

• DLMF

Cites Work

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• A family of the Cauchy type mean-value theorems
• Approximation by Nonlinear Multivariate Sampling Kantorovich Type Operators and Applications to Image Processing
• On Sharp Jensen's Inequality and Some Unusual Applications
• On modular spaces
• Bounds for the normalised Jensen functional
• Applications of sampling Kantorovich operators to thermographic images for seismic engineering

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