Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means

Yu-Ming Chu, Shan-Shan Wang and Cheng Zong

Abstract and Applied Analysis, 2011, vol. 2011, issue 1

Abstract: We find the least value λ ∈ (0, 1) and the greatest value p = p(α) such that αH(a, b) + (1 − α)L(a, b) > Mp(a, b) for α ∈ [λ, 1) and all a, b > 0 with a ≠ b, where H(a, b), L(a, b), and Mp(a, b) are the harmonic, logarithmic, and p‐th power means of two positive numbers a and b, respectively.

Date: 2011
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https://doi.org/10.1155/2011/520648

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:520648

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