EXACT UPPER AND LOWER BOUNDS ON THE DIFFERENCE BETWEEN THE ARITHMETIC AND GEOMETRIC MEANS

DOI10.1017/S0004972715000350zbMath1318.60029arXiv1503.00345MaRDI QIDQ5501759

Iosif Pinelis

Publication date: 14 August 2015

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.00345

zbMATH Keywords

arithmetic meangeometric meanJensen inequalityexact boundsreverse Jensen inequalityTchebycheff-Markoff systems

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Optimality conditions and duality in mathematical programming (90C46) Inequalities for sums, series and integrals (26D15)

Related Items (3)

Randomized Algorithms for Lexicographic Inference ⋮ Comparison of arithmetic, geometric, and harmonic means ⋮ Exact converses to a reverse AM-GM inequality, with applications to sums of independent random variables and (super)martingales

Cites Work

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• An asymptotically Gaussian bound on the Rademacher tails
• A Better Bound on the Variance
• Upper bounds for the variances of certain random variables
• SOME REVERSES OF THE JENSEN INEQUALITY WITH APPLICATIONS

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