Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means
We find the least value λ∈(0,1) and the greatest value p=p(α) such that αH(a,b)+(1−α)L(a,b)>Mp(a,b) for α∈[λ,1) and all a,b>0 with a≠b, where H(a,b), L(a,b), and Mp(a,b) are the harmonic, logarithmic, and p-th power 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: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/520648 |
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| _version_ | 1832555100349923328 |
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| author | Yu-Ming Chu Shan-Shan Wang Cheng Zong |
| author_facet | Yu-Ming Chu Shan-Shan Wang Cheng Zong |
| author_sort | Yu-Ming Chu |
| collection | DOAJ |
| description | We find the least value λ∈(0,1) and the greatest value p=p(α) such that αH(a,b)+(1−α)L(a,b)>Mp(a,b) for α∈[λ,1) and all a,b>0 with a≠b, where H(a,b), L(a,b), and Mp(a,b) are the harmonic,
logarithmic, and p-th power means of two positive numbers a and b, respectively. |
| format | Article |
| id | doaj-art-3189705308ef4f4385cd333598149897 |
| 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-3189705308ef4f4385cd3335981498972025-02-03T05:49:31ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/520648520648Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic MeansYu-Ming Chu0Shan-Shan Wang1Cheng Zong2Department of Mathematics, Huzhou Teachers College, Huzhou 313000, ChinaSchool of Science, Hangzhou Normal University, Hangzhou 310012, ChinaSchool of Science, Hangzhou Normal University, Hangzhou 310012, ChinaWe find the least value λ∈(0,1) and the greatest value p=p(α) such that αH(a,b)+(1−α)L(a,b)>Mp(a,b) for α∈[λ,1) and all a,b>0 with a≠b, where H(a,b), L(a,b), and Mp(a,b) are the harmonic, logarithmic, and p-th power means of two positive numbers a and b, respectively.http://dx.doi.org/10.1155/2011/520648 |
| spellingShingle | Yu-Ming Chu Shan-Shan Wang Cheng Zong Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means Abstract and Applied Analysis |
| title | Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means |
| title_full | Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means |
| title_fullStr | Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means |
| title_full_unstemmed | Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means |
| title_short | Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means |
| title_sort | optimal lower power mean bound for the convex combination of harmonic and logarithmic means |
| url | http://dx.doi.org/10.1155/2011/520648 |
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