Optimal bounds for Toader mean in terms of arithmetic and contraharmonic means

DOI10.7153/JMI-07-68zbMath1298.26098OpenAlexW2312752426MaRDI QIDQ2879473

Ying-Qing Song, Dandan Yan, Wei-Dong Jiang, Yu-Ming Chu

Publication date: 2 September 2014

Published in: Journal of Mathematical Inequalities (Search for Journal in Brave)

Full work available at URL: http://files.ele-math.com/articles/jmi-07-68.pdf

zbMATH Keywords

arithmetic meancomplete elliptic integralscontraharmonic meanToader mean

Mathematics Subject Classification ID

Means (26E60) Elliptic functions and integrals (33E05)

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Sharp approximations for the complete elliptic integrals of the second kind by one-parameter means ⋮ Optimal convex combination bounds of geometric and Neuman means for Toader-type mean ⋮ Sharp bounds for a special quasi-arithmetic mean in terms of arithmetic and geometric means with two parameters ⋮ Sharp bounds for Toader mean in terms of arithmetic and second contraharmonic means ⋮ On approximating the Toader mean by other bivariate means ⋮ Optimal evaluation of a Toader-type mean by power mean ⋮ A double inequality for an integral mean in terms of the exponential and logarithmic means ⋮ Optimal inequalities for bounding Toader mean by arithmetic and quadratic means ⋮ Monotonicity rule for the quotient of two functions and its application ⋮ High accuracy asymptotic bounds for the complete elliptic integral of the second kind ⋮ Sharp bounds for the Toader mean in terms of arithmetic and geometric means ⋮ Infinite series formula for Hübner upper bound function with applications to Hersch-Pfluger distortion function ⋮ On approximating the modified Bessel function of the first kind and Toader-Qi mean ⋮ Sharp bounds for Toader mean in terms of arithmetic, quadratic, and Neuman means

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