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Zbl 1217.26040
Chu, Yu-Ming; Wang, Shan-Shan; Zong, Cheng
Optimal lower power mean bound for the convex combination of harmonic and logarithmic means.
(English)
[J] Abstr. Appl. Anal. 2011, Article ID 520648, 9 p. (2011). ISSN 1085-3375; ISSN 1687-0409/e

Summary: We find the least value $\lambda \in (0, 1)$ and the greatest value $p = p(\alpha)$ such that $\alpha H(a, b) + (1 - \alpha)L(a, b) > M_p (a, b)$ for $\alpha \in [\lambda, 1)$ and all $a, b > 0$ with $a \neq b$, where $H(a, b)$, $L(a, b)$, and $M_p(a, b)$ are the harmonic, logarithmic, and $p$-th power means of two positive numbers $a$ and $b$, respectively.
MSC 2000:
*26D15 Inequalities for sums, series and integrals of real functions

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