Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean
For 1<r<+∞, we find the least value α and the greatest value β such that the inequality Hα(a,b)<Ar(a,b)<Hβ(a,b) holds for all a,b>0 with a≠b. Here, Hω(a,b) and Ar(a,b) are the generalized Heronian and the 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/10.1155/2011/679201 |
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| _version_ | 1832563981449953280 |
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| author | Hongya Gao Jianling Guo Wanguo Yu |
| author_facet | Hongya Gao Jianling Guo Wanguo Yu |
| author_sort | Hongya Gao |
| collection | DOAJ |
| description | For 1<r<+∞, we find the least value α and the greatest value β such
that the inequality Hα(a,b)<Ar(a,b)<Hβ(a,b) holds for all a,b>0 with a≠b. Here, Hω(a,b) and Ar(a,b) are the generalized Heronian
and the power means of two positive numbers a and b, respectively. |
| format | Article |
| id | doaj-art-3eb6de600f4248859f23d31428804de5 |
| 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-3eb6de600f4248859f23d31428804de52025-02-03T01:12:05ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/679201679201Sharp Bounds for Power Mean in Terms of Generalized Heronian MeanHongya Gao0Jianling Guo1Wanguo Yu2College of Mathematics and Computer Science, Hebei University, Baoding 071002, ChinaCollege of Mathematics and Computer Science, Hebei University, Baoding 071002, ChinaCollege of Mathematics and Computer Science, Hebei University, Baoding 071002, ChinaFor 1<r<+∞, we find the least value α and the greatest value β such that the inequality Hα(a,b)<Ar(a,b)<Hβ(a,b) holds for all a,b>0 with a≠b. Here, Hω(a,b) and Ar(a,b) are the generalized Heronian and the power means of two positive numbers a and b, respectively.http://dx.doi.org/10.1155/2011/679201 |
| spellingShingle | Hongya Gao Jianling Guo Wanguo Yu Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean Abstract and Applied Analysis |
| title | Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean |
| title_full | Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean |
| title_fullStr | Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean |
| title_full_unstemmed | Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean |
| title_short | Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean |
| title_sort | sharp bounds for power mean in terms of generalized heronian mean |
| url | http://dx.doi.org/10.1155/2011/679201 |
| work_keys_str_mv | AT hongyagao sharpboundsforpowermeanintermsofgeneralizedheronianmean AT jianlingguo sharpboundsforpowermeanintermsofgeneralizedheronianmean AT wanguoyu sharpboundsforpowermeanintermsofgeneralizedheronianmean |