Multidimensional Hermite-Hadamard inequalities and the convex order

DOI10.1016/j.jmaa.2005.12.018zbMath1112.26020OpenAlexW1985744125MaRDI QIDQ855635

Jesús De La Cal, Javier Cárcamo

Publication date: 7 December 2006

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2005.12.018

zbMATH Keywords

Jensen's inequalitypolytopeconvex bodyuniform distributionChoquet theoryrepresentation systemH-majorant

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15)

Related Items (16)

Some Hermite–Hadamard type integral inequalities for multidimensional general preinvex stochastic processes ⋮ Improved bounds for Hermite-Hadamard inequalities in higher dimensions ⋮ Some integral inequalities of the Hermite-Hadamard type for s-convex stochastic processes on n-coordinates ⋮ Some Hermite-Hadamard type integral inequalities for convex functions defined on convex bodies in \(\mathbb{R}^n\) ⋮ Some Extensions of Preinvexity for Stochastic Processes ⋮ On Hermite-Hadamard-type inequalities for systems of partial differential inequalities in the plane ⋮ On Hermite-Hadamard-Type Inequalities for Subharmonic Functions Over Circular Ring Domains ⋮ On a generalization of the Hermite-Hadamard inequality and applications in convex geometry ⋮ On Some Recent Applications of Stochastic Convex Ordering Theorems to Some Functional Inequalities for Convex Functions: A Survey ⋮ A family of mappings associated with Hadamard's inequality on a hypercube ⋮ Estimating the average of functions with convexity properties by means of a new center ⋮ A dimension-free Hermite–Hadamard inequality via gradient estimates for the torsion function ⋮ Towards optimal gradient bounds for the torsion function in the plane ⋮ The Hermite-Hadamard inequality in higher dimensions ⋮ A general multidimensional Hermite-Hadamard type inequality ⋮ Some triple integral inequalities for functions defined on three-dimensional bodies via Gauss-Ostrogradsky identity

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• A general Ostrowski-type inequality
• Projecting the surface measure of the sphere of \({\ell}_p^n\)
• Choquet theory for signed measures
• A best possible Hadamard inequality
• On Hadamard's inequality for the convex mappings defined on a ball in the space and applications
• The Hermite-Hadamard inequality for convex functions of a vector variable

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