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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 830585, 11 pages
doi:10.1155/2012/830585
Research Article
Inequalities between Arithmetic-Geometric, Gini, and Toader Means
Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
Received 24 August 2011; Accepted 20 October 2011
Academic Editor: Muhammad Aslam Noor
Copyright © 2012 Yu-Ming Chu and Miao-Kun Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We find the greatest values , and least values , such that the double inequalities and hold for all with and present some new bounds for the complete elliptic integrals. Here , , and are the arithmetic-geometric, Toader, and th Gini means of two positive numbers and , respectively.