## Abstract and Applied Analysis

### Inequalities between Arithmetic-Geometric, Gini, and Toader Means

#### Abstract

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) and ${S}_{{p}_{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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 830585, 11 pages.

Dates
First available in Project Euclid: 15 February 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1329337684

Digital Object Identifier
doi:10.1155/2012/830585

Mathematical Reviews number (MathSciNet)
MR2861493

Zentralblatt MATH identifier
1229.26031

#### Citation

Chu, Yu-Ming; Wang, Miao-Kun. Inequalities between Arithmetic-Geometric, Gini, and Toader Means. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 830585, 11 pages. doi:10.1155/2012/830585. https://projecteuclid.org/euclid.aaa/1329337684

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