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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/830585 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849683973641338880 |
|---|---|
| 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. |
| format | Article |
| id | doaj-art-cbe3d679afb14153883872a4ed40bbf9 |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| 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 |