Open Access

The optimization for the inequalities of power means

Journal of Inequalities and Applications20062006:46782

DOI: 10.1155/JIA/2006/46782

Received: 14 November 2005

Accepted: 14 July 2006

Published: 19 October 2006


Let be the th power mean of a sequence of positive real numbers, where , and . In this paper, we will state the important background and meaning of the inequality ; 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.


Authors’ Affiliations

Department of Mathematics and Computer Science, Chengdu University


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© J.Wen andW.-L.Wang. 2006

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