A Best Possible Double Inequality for Power Mean
We answer the question: for any p,q∈ℝ with p≠q and p≠-q, what are the greatest value λ=λ(p,q) and the least value μ=μ(p,q), such that the double inequality Mλ(a,b)<Mp(a,b)Mq(a,b)<Mμ(a,b) holds for all a,b>0 with a≠b? Where Mp(a,b) is the pth power mean of two positive numbers a and b....
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/379785 |
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| author | Yong-Min Li Bo-Yong Long Yu-Ming Chu |
| author_facet | Yong-Min Li Bo-Yong Long Yu-Ming Chu |
| author_sort | Yong-Min Li |
| collection | DOAJ |
| description | We answer the question: for any p,q∈ℝ with p≠q and p≠-q, what are the greatest value λ=λ(p,q) and the least value μ=μ(p,q), such that the double inequality Mλ(a,b)<Mp(a,b)Mq(a,b)<Mμ(a,b) holds for all a,b>0 with a≠b? Where Mp(a,b) is the pth power mean of two positive numbers a and b. |
| format | Article |
| id | doaj-art-ecc0777b56c64c86a8fd0fffc0c3fa01 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-ecc0777b56c64c86a8fd0fffc0c3fa012025-02-03T00:59:45ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/379785379785A Best Possible Double Inequality for Power MeanYong-Min Li0Bo-Yong Long1Yu-Ming Chu2Department of Mathematics, Huzhou Teachers College, Huzhou 313000, ChinaSchool of Mathematics Science, Anhui University, Hefei 230039, ChinaDepartment of Mathematics, Huzhou Teachers College, Huzhou 313000, ChinaWe answer the question: for any p,q∈ℝ with p≠q and p≠-q, what are the greatest value λ=λ(p,q) and the least value μ=μ(p,q), such that the double inequality Mλ(a,b)<Mp(a,b)Mq(a,b)<Mμ(a,b) holds for all a,b>0 with a≠b? Where Mp(a,b) is the pth power mean of two positive numbers a and b.http://dx.doi.org/10.1155/2012/379785 |
| spellingShingle | Yong-Min Li Bo-Yong Long Yu-Ming Chu A Best Possible Double Inequality for Power Mean Journal of Applied Mathematics |
| title | A Best Possible Double Inequality for Power Mean |
| title_full | A Best Possible Double Inequality for Power Mean |
| title_fullStr | A Best Possible Double Inequality for Power Mean |
| title_full_unstemmed | A Best Possible Double Inequality for Power Mean |
| title_short | A Best Possible Double Inequality for Power Mean |
| title_sort | best possible double inequality for power mean |
| url | http://dx.doi.org/10.1155/2012/379785 |
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