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- W2393524601 abstract "Let ∏~k_n(a)=(∏1i_1...i_k≤nD)k~(-1)∑~k_(j=1)a_(i_j))~(1/(nk)),A(a)=1n∑~n_(i=1)a_i,G(a)=(∏~n_(i=1)a_i)~(1/n)are the third symmetric mean of k dgree, the arithmatic mean and the geometric mean of a_1,...,a_n. By means of decsending dimension method, we have proved that the maximun of p is p_n=n-2n-1and the minimum of q is q_n=n(n-2)~(1-1n)(n-1)~(1n-2)so that the inequality ~p~(1-p)≤∏~(n-1)_n(a)≤q A(a)+(1-q)G(a) is held, where, a∈R~n_(++),n≥3. As applications, our results are applied to positive difinite matrice and simplexes." @default.
- W2393524601 created "2016-06-24" @default.
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- W2393524601 date "2004-01-01" @default.
- W2393524601 modified "2023-09-26" @default.
- W2393524601 title "An Optimizing Inequality Involving the Third Symmetric Mean and Their Applications" @default.
- W2393524601 hasPublicationYear "2004" @default.
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