An Optimal Double Inequality between Seiffert and Geometric Means
For α,β∈(0,1/2) we prove that the double inequality G(αa+(1−α)b,αb+(1−α)a)<P(a,b)<G(βa+(1−β)b,βb+(1−β)a) holds for all a,b>0 with a≠b if and only if α≤(1−1−4/π2)/2 and β≥(3−3)/6. Here, G(a,b) and P(a,b) denote the geometric and Seiffert means of two positive numbers a and b, respectively....
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/261237 |
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| author | Yu-Ming Chu Miao-Kun Wang Zi-Kui Wang |
| author_facet | Yu-Ming Chu Miao-Kun Wang Zi-Kui Wang |
| author_sort | Yu-Ming Chu |
| collection | DOAJ |
| description | For α,β∈(0,1/2) we prove that the double inequality G(αa+(1−α)b,αb+(1−α)a)<P(a,b)<G(βa+(1−β)b,βb+(1−β)a) holds for all a,b>0 with a≠b if and only if α≤(1−1−4/π2)/2 and β≥(3−3)/6. Here, G(a,b) and P(a,b) denote the geometric and Seiffert means of two positive numbers a and b, respectively. |
| format | Article |
| id | doaj-art-cad4f1d8f6a34001b7cbbef7c9fd00fd |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-cad4f1d8f6a34001b7cbbef7c9fd00fd2025-08-20T02:19:38ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/261237261237An Optimal Double Inequality between Seiffert and Geometric MeansYu-Ming Chu0Miao-Kun Wang1Zi-Kui Wang2Department of Mathematics, Huzhou Teachers College, Huzhou 313000, ChinaDepartment of Mathematics, Huzhou Teachers College, Huzhou 313000, ChinaDepartment of Mathematics, Hangzhou Normal University, Hangzhou 310012, ChinaFor α,β∈(0,1/2) we prove that the double inequality G(αa+(1−α)b,αb+(1−α)a)<P(a,b)<G(βa+(1−β)b,βb+(1−β)a) holds for all a,b>0 with a≠b if and only if α≤(1−1−4/π2)/2 and β≥(3−3)/6. Here, G(a,b) and P(a,b) denote the geometric and Seiffert means of two positive numbers a and b, respectively.http://dx.doi.org/10.1155/2011/261237 |
| spellingShingle | Yu-Ming Chu Miao-Kun Wang Zi-Kui Wang An Optimal Double Inequality between Seiffert and Geometric Means Journal of Applied Mathematics |
| title | An Optimal Double Inequality between Seiffert and Geometric Means |
| title_full | An Optimal Double Inequality between Seiffert and Geometric Means |
| title_fullStr | An Optimal Double Inequality between Seiffert and Geometric Means |
| title_full_unstemmed | An Optimal Double Inequality between Seiffert and Geometric Means |
| title_short | An Optimal Double Inequality between Seiffert and Geometric Means |
| title_sort | optimal double inequality between seiffert and geometric means |
| url | http://dx.doi.org/10.1155/2011/261237 |
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