The optimization for the inequalities of power means

  • Jiajin Wen
  • Wan-Lan Wang
Open Access
Research Article


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


Real Number Open Problem Mathematical Analysis Positive Real Number Symmetrical Polynomial 
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Copyright information

© J.Wen andW.-L.Wang. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceChengdu UniversityChengdu, SichuanChina

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