Sharp Power Mean Bounds for the One-Parameter Harmonic Mean
We present the best possible parameters α=α(r) and β=β(r) such that the double inequality Mα(a,b)<Hr(a,b)<Mβ(a,b) holds for all r∈(0, 1/2) and a, b>0 with a≠b, where Mp(a, b)=[(ap+bp)/2]1/p (p≠0) and M0(a, b)=ab and Hr(a, b)=2[ra+(1-r)b][rb+(1-r)a]/(a+b) are the power and one-parameter har...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/517647 |
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| author | Yu-Ming Chu Li-Min Wu Ying-Qing Song |
| author_facet | Yu-Ming Chu Li-Min Wu Ying-Qing Song |
| author_sort | Yu-Ming Chu |
| collection | DOAJ |
| description | We present the best possible parameters α=α(r) and β=β(r) such that the double inequality Mα(a,b)<Hr(a,b)<Mβ(a,b) holds for all r∈(0, 1/2) and a, b>0 with a≠b, where Mp(a, b)=[(ap+bp)/2]1/p (p≠0) and M0(a, b)=ab and Hr(a, b)=2[ra+(1-r)b][rb+(1-r)a]/(a+b) are the power and one-parameter harmonic means of a and b, respectively. |
| format | Article |
| id | doaj-art-ce8a6ea2f87d4a3e9459d273ac9e89d5 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-ce8a6ea2f87d4a3e9459d273ac9e89d52025-02-03T01:07:32ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/517647517647Sharp Power Mean Bounds for the One-Parameter Harmonic MeanYu-Ming Chu0Li-Min Wu1Ying-Qing Song2School of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, ChinaDepartment of Mathematics, Huzhou University, Huzhou 313000, ChinaSchool of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, ChinaWe present the best possible parameters α=α(r) and β=β(r) such that the double inequality Mα(a,b)<Hr(a,b)<Mβ(a,b) holds for all r∈(0, 1/2) and a, b>0 with a≠b, where Mp(a, b)=[(ap+bp)/2]1/p (p≠0) and M0(a, b)=ab and Hr(a, b)=2[ra+(1-r)b][rb+(1-r)a]/(a+b) are the power and one-parameter harmonic means of a and b, respectively.http://dx.doi.org/10.1155/2015/517647 |
| spellingShingle | Yu-Ming Chu Li-Min Wu Ying-Qing Song Sharp Power Mean Bounds for the One-Parameter Harmonic Mean Journal of Function Spaces |
| title | Sharp Power Mean Bounds for the One-Parameter Harmonic Mean |
| title_full | Sharp Power Mean Bounds for the One-Parameter Harmonic Mean |
| title_fullStr | Sharp Power Mean Bounds for the One-Parameter Harmonic Mean |
| title_full_unstemmed | Sharp Power Mean Bounds for the One-Parameter Harmonic Mean |
| title_short | Sharp Power Mean Bounds for the One-Parameter Harmonic Mean |
| title_sort | sharp power mean bounds for the one parameter harmonic mean |
| url | http://dx.doi.org/10.1155/2015/517647 |
| work_keys_str_mv | AT yumingchu sharppowermeanboundsfortheoneparameterharmonicmean AT liminwu sharppowermeanboundsfortheoneparameterharmonicmean AT yingqingsong sharppowermeanboundsfortheoneparameterharmonicmean |