Abstract and Applied Analysis

Inequalities between Arithmetic-Geometric, Gini, and Toader Means

Yu-Ming Chu and Miao-Kun Wang

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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 ) < 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 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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