Abstract and Applied Analysis

Inequalities between Arithmetic-Geometric, Gini, and Toader Means

Yu-Ming Chu and Miao-Kun Wang

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We find the greatest values ${p}_{1}$, ${p}_{2}$ and least values ${q}_{1}$, ${q}_{2}$ such that the double inequalities ${S}_{{p}_{1}}(a,b)<M(a,b)<{S}_{{q}_{1}}(a,b)$ and ${S}_{{p}_{2}}(a,b)<T(a,b)<{S}_{{q}_{2}}(a,b)$ hold for all $a,b>0$ with $a\ne b$ and present some new bounds for the complete elliptic integrals. Here $M(a,b)$, $T(a,b)$, and ${S}_{p}(a,b)$ are the arithmetic-geometric, Toader, and $p$th Gini means of two positive numbers $a$ and $b$, respectively.

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Abstr. Appl. Anal. Volume 2012, Special Issue (2012), Article ID830585, 11 pages.

First available: 15 February 2012

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Chu, Yu-Ming; Wang, Miao-Kun. Inequalities between Arithmetic-Geometric, Gini, and Toader Means. Abstract and Applied Analysis 2012, Special Issue (2012), 1--11. doi:10.1155/2012/830585. http://projecteuclid.org/euclid.aaa/1329337684.

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