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**Optimal inequalities for power means.**
*(English)*
Zbl 1244.26044

Summary: We present the best possible power mean bounds for the product \(M^\alpha_p(a, b) M^{1-\alpha}_{-p}(a, b)\) for any \(p > 0, \alpha \in (0, 1)\), and all \(a, b > 0\) with \(a \neq b\). Here, \(M_p(a, b)\) is the \(p\)th power mean of two positive numbers \(a\) and \(b\).

### MSC:

26D15 | Inequalities for sums, series and integrals |

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\textit{Y.-M. Li} et al., J. Appl. Math. 2012, Article ID 182905, 8 p. (2012; Zbl 1244.26044)

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### References:

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