The optimization for the inequalities of power means
<p/> <p>Let <inline-formula><graphic file="1029-242X-2006-46782-i1.gif"/></inline-formula> be the <inline-formula><graphic file="1029-242X-2006-46782-i2.gif"/></inline-formula>th power mean of a sequence <inline-formula><gr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2006-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2006/46782 |
| _version_ | 1819062469943885824 |
|---|---|
| author | Wen Jiajin Wang Wan-Lan |
| author_facet | Wen Jiajin Wang Wan-Lan |
| author_sort | Wen Jiajin |
| collection | DOAJ |
| description | <p/> <p>Let <inline-formula><graphic file="1029-242X-2006-46782-i1.gif"/></inline-formula> be the <inline-formula><graphic file="1029-242X-2006-46782-i2.gif"/></inline-formula>th power mean of a sequence <inline-formula><graphic file="1029-242X-2006-46782-i3.gif"/></inline-formula> of positive real numbers, where <inline-formula><graphic file="1029-242X-2006-46782-i4.gif"/></inline-formula>, and <inline-formula><graphic file="1029-242X-2006-46782-i5.gif"/></inline-formula>. In this paper, we will state the important background and meaning of the inequality <inline-formula><graphic file="1029-242X-2006-46782-i6.gif"/></inline-formula>; a necessary and sufficient condition and another interesting sufficient condition that the foregoing inequality holds are obtained; an open problem posed by Wang et al. in 2004 is solved and generalized; a rulable criterion of the semipositivity of homogeneous symmetrical polynomial is also obtained. Our methods used are the procedure of descending dimension and theory of majorization; and apply techniques of mathematical analysis and permanents in algebra.</p> |
| first_indexed | 2024-12-21T14:59:17Z |
| format | Article |
| id | doaj.art-9b8f0818ca9c43c2a2b6f2027b3f2528 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-21T14:59:17Z |
| publishDate | 2006-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-9b8f0818ca9c43c2a2b6f2027b3f25282022-12-21T18:59:38ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2006-01-012006146782The optimization for the inequalities of power meansWen JiajinWang Wan-Lan<p/> <p>Let <inline-formula><graphic file="1029-242X-2006-46782-i1.gif"/></inline-formula> be the <inline-formula><graphic file="1029-242X-2006-46782-i2.gif"/></inline-formula>th power mean of a sequence <inline-formula><graphic file="1029-242X-2006-46782-i3.gif"/></inline-formula> of positive real numbers, where <inline-formula><graphic file="1029-242X-2006-46782-i4.gif"/></inline-formula>, and <inline-formula><graphic file="1029-242X-2006-46782-i5.gif"/></inline-formula>. In this paper, we will state the important background and meaning of the inequality <inline-formula><graphic file="1029-242X-2006-46782-i6.gif"/></inline-formula>; a necessary and sufficient condition and another interesting sufficient condition that the foregoing inequality holds are obtained; an open problem posed by Wang et al. in 2004 is solved and generalized; a rulable criterion of the semipositivity of homogeneous symmetrical polynomial is also obtained. Our methods used are the procedure of descending dimension and theory of majorization; and apply techniques of mathematical analysis and permanents in algebra.</p>http://www.journalofinequalitiesandapplications.com/content/2006/46782 |
| spellingShingle | Wen Jiajin Wang Wan-Lan The optimization for the inequalities of power means Journal of Inequalities and Applications |
| title | The optimization for the inequalities of power means |
| title_full | The optimization for the inequalities of power means |
| title_fullStr | The optimization for the inequalities of power means |
| title_full_unstemmed | The optimization for the inequalities of power means |
| title_short | The optimization for the inequalities of power means |
| title_sort | optimization for the inequalities of power means |
| url | http://www.journalofinequalitiesandapplications.com/content/2006/46782 |
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