A note on Schur-convexity of extended mean values

DOI10.1216/rmjm/1181069663zbMath1104.26013OpenAlexW2075492385MaRDI QIDQ2496915

Feng Qi

Publication date: 25 July 2006

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181069663

zbMATH Keywords

inequalitiesStolarsky means

Mathematics Subject Classification ID

Convexity of real functions of several variables, generalizations (26B25) Other analytical inequalities (26D20) Inequalities involving other types of functions (26D07)

Related Items (12)

Completely monotonic degree of a function involving trigamma and tetragamma functions ⋮ Necessary and sufficient conditions on the Schur convexity of a bivariate mean ⋮ The Function (b x − a x )∕x: Ratio’s Properties ⋮ Schur convexity of the generalized geometric Bonferroni mean and the relevant inequalities ⋮ Schur convexity of Bonferroni harmonic mean ⋮ Schur-convexity of the Catalan-Qi function related to the Catalan numbers ⋮ Schur-convexity of two types of one-parameter mean values in \(n\) variables ⋮ Schur convexity for a class of symmetric functions ⋮ Schur-convexity of averages of convex functions ⋮ Necessary and sufficient conditions for Schur geometrical convexity of the four-parameter homogeneous means ⋮ Schur convexity properties for a class of symmetric functions with applications ⋮ Solution of an open problem for Schur convexity or concavity of the Gini mean values

Cites Work

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• Notes on the Schur-convexity of the extended mean values
• Extended mean values. II
• Inequalities for differences of powers
• Convex functions, partial orderings, and statistical applications
• A simple proof of monotonicity for extended mean values
• Refinements and extensions of an inequality. III
• A new proof of monotonicity for extended mean values
• Logarithmic convexity of extended mean values
• Generalizations of the Logarithmic Mean
• Extended Mean Values
• The function (𝑏^{𝑥}-𝑎^{𝑥})/𝑥: Inequalities and properties
• Generalized weighted mean values with two parameters
• New proofs of weighted power mean inequalities and monotonicity for generalized weighted mean values
• Note on monotonicity of generalized weighted mean values
• A note on Schur-convex functions

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