Optimal Lehmer mean bounds for the combinations of identric and logarithmic means

DOI10.1155/2013/852516zbMath1298.26097OpenAlexW1974907859WikidataQ58920760 ScholiaQ58920760MaRDI QIDQ463186

Xu-Hui Shen, Yu-Ming Chu, Wei-Ming Gong

Publication date: 16 October 2014

Published in: Chinese Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/852516

zbMATH Keywords

logarithmic meanarithmetic-geometric meanGauss' hypergeometric function \(_2F_1\)

Mathematics Subject Classification ID

Means (26E60)

Cites Work

• A note on some inequalities for means
• On the identric and logarithmic means
• Ungleichungen für Mittelwerte. (Inequalities for means)
• Ungleichungen für \((e/a)^ a(b/e)^ b\). (Inequalities for \((e/a)^ a(b/e)^ b)\)
• Inequalities for means
• Inequalities for means in two variables
• Remark on inequalities between Hölder and Lehmer means
• On certain inequalities for means
• Two inequalities for means
• On certain inequalities for means. II
• Hölder means, Lehmer means, and \(x^{-1} \log \cosh x\)
• Total Positivity of Mean Values and Hypergeometric Functions
• The Logarithmic Mean in n Variables
• The Geometric, Logarithmic, and Arithmetic Mean Inequality
• The Power and Generalized Logarithmic Means
• The Power Mean and the Logarithmic Mean
• Functional Equations Involving the Logarithmic Mean
• A reverse Hölder type inequality for the logarithmic mean and generalizations
• Algorithms Involving Arithmetic and Geometric Means
• The Logarithmic Mean
• A Class of Mean Value Functions
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)
• On certain inequalities for means. III
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