Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means
We answer the question: for α∈(0,1), what are the greatest value p and the least value q such that the double inequality Mp(a,b)<Pα(a,b)G1−α(a,b)<Mq(a,b) holds for all a,b>0 with a≠b. Here, Mp(a,b), P(a,b), and G(a,b) denote the power of order p, Seiffert, and geometric means of two positi...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/108920 |
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| author | Yu-Ming Chu Ye-Fang Qiu Miao-Kun Wang |
| author_facet | Yu-Ming Chu Ye-Fang Qiu Miao-Kun Wang |
| author_sort | Yu-Ming Chu |
| collection | DOAJ |
| description | We answer the question: for α∈(0,1), what are the greatest value p
and the least value q such that the double inequality Mp(a,b)<Pα(a,b)G1−α(a,b)<Mq(a,b) holds for all a,b>0 with a≠b. Here, Mp(a,b), P(a,b), and G(a,b) denote the power of order p, Seiffert, and geometric means of two positive numbers a and b, respectively. |
| format | Article |
| id | doaj-art-e66d28d539054282a1b2e31a033dce0b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e66d28d539054282a1b2e31a033dce0b2025-02-03T01:27:16ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/108920108920Sharp Power Mean Bounds for the Combination of Seiffert and Geometric MeansYu-Ming Chu0Ye-Fang Qiu1Miao-Kun Wang2Department of Mathematics, Huzhou Teachers College, Huzhou 313000, ChinaDepartment of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, ChinaDepartment of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, ChinaWe answer the question: for α∈(0,1), what are the greatest value p and the least value q such that the double inequality Mp(a,b)<Pα(a,b)G1−α(a,b)<Mq(a,b) holds for all a,b>0 with a≠b. Here, Mp(a,b), P(a,b), and G(a,b) denote the power of order p, Seiffert, and geometric means of two positive numbers a and b, respectively.http://dx.doi.org/10.1155/2010/108920 |
| spellingShingle | Yu-Ming Chu Ye-Fang Qiu Miao-Kun Wang Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means Abstract and Applied Analysis |
| title | Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means |
| title_full | Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means |
| title_fullStr | Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means |
| title_full_unstemmed | Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means |
| title_short | Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means |
| title_sort | sharp power mean bounds for the combination of seiffert and geometric means |
| url | http://dx.doi.org/10.1155/2010/108920 |
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