A Sharp Double Inequality between Harmonic and Identric Means
We find the greatest value p and the least value q in (0,1/2) such that the double inequality H(pa+(1-p)b,pb+(1-p)a)<I(a,b)<H(qa+(1-q)b,qb+(1-q)a) holds for all a,b>0 with a≠b. Here, H(a,b), and I(a,b) denote the harmonic and identric means of two positive numbers a and b, respectively.
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/657935 |
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| _version_ | 1849400445464739840 |
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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 | We find the greatest value p and the least value q in (0,1/2) such that the double inequality H(pa+(1-p)b,pb+(1-p)a)<I(a,b)<H(qa+(1-q)b,qb+(1-q)a) holds for all a,b>0 with a≠b. Here, H(a,b), and I(a,b) denote the harmonic and identric means of two positive numbers a and b, respectively. |
| format | Article |
| id | doaj-art-85d235db56be4b02a9d69ad7cfa0888d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-85d235db56be4b02a9d69ad7cfa0888d2025-08-20T03:38:03ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/657935657935A Sharp Double Inequality between Harmonic and Identric 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, ChinaWe find the greatest value p and the least value q in (0,1/2) such that the double inequality H(pa+(1-p)b,pb+(1-p)a)<I(a,b)<H(qa+(1-q)b,qb+(1-q)a) holds for all a,b>0 with a≠b. Here, H(a,b), and I(a,b) denote the harmonic and identric means of two positive numbers a and b, respectively.http://dx.doi.org/10.1155/2011/657935 |
| spellingShingle | Yu-Ming Chu Miao-Kun Wang Zi-Kui Wang A Sharp Double Inequality between Harmonic and Identric Means Abstract and Applied Analysis |
| title | A Sharp Double Inequality between Harmonic and Identric Means |
| title_full | A Sharp Double Inequality between Harmonic and Identric Means |
| title_fullStr | A Sharp Double Inequality between Harmonic and Identric Means |
| title_full_unstemmed | A Sharp Double Inequality between Harmonic and Identric Means |
| title_short | A Sharp Double Inequality between Harmonic and Identric Means |
| title_sort | sharp double inequality between harmonic and identric means |
| url | http://dx.doi.org/10.1155/2011/657935 |
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