Inequalities between Arithmetic-Geometric, Gini, and Toader Means

We find the greatest values p1, p2 and least values q1, q2 such that the double inequalities Sp1(a,b)<M(a,b)<Sq1(a,b) and Sp2(a,b)<T(a,b)<Sq2(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 Sp(a,b) are the arit...

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Main Authors: Yu-Ming Chu, Miao-Kun Wang
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/830585
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author Yu-Ming Chu
Miao-Kun Wang
author_facet Yu-Ming Chu
Miao-Kun Wang
author_sort Yu-Ming Chu
collection DOAJ
description We find the greatest values p1, p2 and least values q1, q2 such that the double inequalities Sp1(a,b)<M(a,b)<Sq1(a,b) and Sp2(a,b)<T(a,b)<Sq2(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 Sp(a,b) are the arithmetic-geometric, Toader, and pth Gini means of two positive numbers a and b, respectively.
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spelling doaj-art-cbe3d679afb14153883872a4ed40bbf92025-08-20T03:23:37ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/830585830585Inequalities between Arithmetic-Geometric, Gini, and Toader MeansYu-Ming Chu0Miao-Kun Wang1Department of Mathematics, Huzhou Teachers College, Huzhou 313000, ChinaDepartment of Mathematics, Huzhou Teachers College, Huzhou 313000, ChinaWe find the greatest values p1, p2 and least values q1, q2 such that the double inequalities Sp1(a,b)<M(a,b)<Sq1(a,b) and Sp2(a,b)<T(a,b)<Sq2(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 Sp(a,b) are the arithmetic-geometric, Toader, and pth Gini means of two positive numbers a and b, respectively.http://dx.doi.org/10.1155/2012/830585
spellingShingle Yu-Ming Chu
Miao-Kun Wang
Inequalities between Arithmetic-Geometric, Gini, and Toader Means
Abstract and Applied Analysis
title Inequalities between Arithmetic-Geometric, Gini, and Toader Means
title_full Inequalities between Arithmetic-Geometric, Gini, and Toader Means
title_fullStr Inequalities between Arithmetic-Geometric, Gini, and Toader Means
title_full_unstemmed Inequalities between Arithmetic-Geometric, Gini, and Toader Means
title_short Inequalities between Arithmetic-Geometric, Gini, and Toader Means
title_sort inequalities between arithmetic geometric gini and toader means
url http://dx.doi.org/10.1155/2012/830585
work_keys_str_mv AT yumingchu inequalitiesbetweenarithmeticgeometricginiandtoadermeans
AT miaokunwang inequalitiesbetweenarithmeticgeometricginiandtoadermeans