The optimization for the inequalities of power means
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.
KeywordsReal Number Open Problem Mathematical Analysis Positive Real Number Symmetrical Polynomial
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