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Journal of Inequalities and Applications
Erschienen in: Journal of Inequalities and Applications 1/2006

Open Access 01.12.2006 | Research Article

The optimization for the inequalities of power means

verfasst von: Jiajin Wen, Wan-Lan Wang

Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2006

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Abstract

Let https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F46782/MediaObjects/13660_2005_Article_1601_IEq1_HTML.gif be the https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F46782/MediaObjects/13660_2005_Article_1601_IEq2_HTML.gif th power mean of a sequence https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F46782/MediaObjects/13660_2005_Article_1601_IEq3_HTML.gif of positive real numbers, where https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F46782/MediaObjects/13660_2005_Article_1601_IEq4_HTML.gif , and https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F46782/MediaObjects/13660_2005_Article_1601_IEq5_HTML.gif . In this paper, we will state the important background and meaning of the inequality https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F46782/MediaObjects/13660_2005_Article_1601_IEq6_HTML.gif ; 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.
Vorheriger Artikel Hardy inequalities in strips on ruled surfaces
Nächster Artikel The Fuglede-Putnam theorem for-quasihyponormal operators

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Metadaten
Titel
The optimization for the inequalities of power means
verfasst von
Jiajin Wen
Wan-Lan Wang
Publikationsdatum
01.12.2006
Verlag
Springer International Publishing
Erschienen in
Journal of Inequalities and Applications / Ausgabe 1/2006
Elektronische ISSN: 1029-242X
DOI
https://doi.org/10.1155/JIA/2006/46782

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