Inequalities between Power Means and Convex Combinations of the Harmonic and Logarithmic Means

Wei-Mao Qian and Zhong-Hua Shen

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

Abstract: We prove that αH(a, b)+(1 − α)L(a, b) > M(1−4α)/3(a, b) for α ∈ (0, 1) and all a, b > 0 with a ≠ b if and only if α ∈ [1/4, 1) and αH(a, b)+(1 − α)L(a, b)

Date: 2012
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https://doi.org/10.1155/2012/471096

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:471096

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