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

Optimal lower power mean bound for the convex combination of harmonic and logarithmic means. (English) Zbl 1217.26040

Abstr. Appl. Anal. 2011, Article ID 520648, 9 p. (2011).
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.

Cited in 7 Documents

MSC:

26D15 Inequalities for sums, series and integrals
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\textit{Y.-M. Chu} et al., Abstr. Appl. Anal. 2011, Article ID 520648, 9 p. (2011; Zbl 1217.26040)
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References:

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