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Gao, Hongya; Guo, Jianling; Yu, Wanguo

Sharp bounds for power mean in terms of generalized Heronian mean. (English) Zbl 1218.26022

Abstr. Appl. Anal. 2011, Article ID 679201, 9 p. (2011).
Summary: For \(1 < r < +\infty\), we find the least value \(\alpha\) and the greatest value \(\beta\) such that the inequality \(H_{\alpha}(a, b) < A_r(a, b) < H_{\beta}(a, b)\) holds for all \(a, b > 0\) with \(a \neq b\). Here, \(H_{\omega}(a, b)\) and \(A_r(a, b)\) are the generalized Heronian and the power means of two positive numbers \(a\) and \(b\), respectively.

Cited in 4 Documents

MSC:

26D15 Inequalities for sums, series and integrals
26E60 Means

Keywords:

power mean; Heronian mean
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\textit{H. Gao} et al., Abstr. Appl. Anal. 2011, Article ID 679201, 9 p. (2011; Zbl 1218.26022)
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