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The optimization for the inequalities of power means
Journal of Inequalities and Applications volume 2006, Article number: 46782 (2006)
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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Wen, J., Wang, WL. The optimization for the inequalities of power means. J Inequal Appl 2006, 46782 (2006). https://doi.org/10.1155/JIA/2006/46782
- Real Number
- Open Problem
- Mathematical Analysis
- Positive Real Number
- Symmetrical Polynomial