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Zbl 1197.26054
Chu, Yu-Ming; Qiu, Ye-Fang; Wang, Miao-Kun
Sharp power mean bounds for the combination of Seiffert and geometric means.
(English)
[J] Abstr. Appl. Anal. 2010, Article ID 108920, 12 p. (2010). ISSN 1085-3375; ISSN 1687-0409/e

Summary: We answer the question: for $\alpha \in (0,1)$, what are the greatest value $p$ and the least value $q$ such that the double inequality $M_{p}(a,b)<P^\alpha(a,b)G^{1-\alpha}(a,b)<M_q(a,b)$ holds for all $a,b>0$ with $a\neq b$. Here, $M_{p}(a,b)$, $P(a,b)$, and $G(a,b)$ denote the power of order $p$, Seiffert, and geometric means of two positive numbers $a$ and $b$, respectively.
MSC 2000:
*26E60 Means

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