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 |
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Hindawi Limited
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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doaj-e66d28d539054282a1b2e31a033dce0b2020-11-24T23:27:21ZengHindawi LimitedAbstract 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yu-Ming Chu Ye-Fang Qiu Miao-Kun Wang |
| 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 |
| author_facet |
Yu-Ming Chu Ye-Fang Qiu Miao-Kun Wang |
| author_sort |
Yu-Ming Chu |
| title |
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_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_sort |
sharp power mean bounds for the combination of seiffert and geometric means |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2010-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2010/108920 |
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AT yumingchu sharppowermeanboundsforthecombinationofseiffertandgeometricmeans AT yefangqiu sharppowermeanboundsforthecombinationofseiffertandgeometricmeans AT miaokunwang sharppowermeanboundsforthecombinationofseiffertandgeometricmeans |
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1725552215490297856 |