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An optimal version of an inequality involving the third symmetric means

✍ Scribed by Jiajin Wen; Jun Yuan; Shufeng Yuan

Book ID
107589289
Publisher
Indian Academy of Sciences
Year
2008
Tongue
English
Weight
143 KB
Volume
118
Category
Article
ISSN
0253-4142

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An optimal power mean inequality for the
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✍ Miao-Kun Wang; Yu-Ming Chu; Ye-Fang Qiu; Song-Liang Qiu πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 214 KB

## a b s t r a c t In this work, we prove that M p (K(r), E (r)) > Ο€ /2 for all r ∈ (0, 1) if and only if p β‰₯ -1/2, where M p (x, y) denotes the power mean of order p of two positive numbers x and y, and K(r) and E (r) denote the complete elliptic integrals of the first and second kinds, respectiv