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The optimization for the inequalities of power means


Let be theth 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.



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Correspondence to Jiajin Wen.

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Wen, J., Wang, WL. The optimization for the inequalities of power means. J Inequal Appl 2006, 46782 (2006).

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  • Real Number
  • Open Problem
  • Mathematical Analysis
  • Positive Real Number
  • Symmetrical Polynomial