关于Hamy平均的一个优化不等式

Optimal inequalities involving Hamy's means

关于n个正数的k次Hamy平均σ_n(a,k)=1/C_n^k sum from 1≤i1<…<ik≤n(multiply from j=1 to k a_(ij))^(1/k),利用最值压缩定理,证明了与Hamy平均、算术平均和几何平均有关的一个双向不等式(A_n(a^(1/k)))^(kp)·(G_n(a^(1/k)))^(k(1-p))≤σ_n(a,k)≤qA_n(a)+(1-q)G_n(a),其中q=n-k/n-1和p=n-k/kn-k为最佳,从而得到一个较理想的优化不等式.

For Hamy＇s means σn（a,k）=1/cnk1≤i1∑1〈…〈ik≤n（k∏j-1aij）1/k of n positive real numbers,the paper proved a double inequality involving arithmetic mean, geometric mean and Hamy＇s mean （An（a1/k））kp·（Gn（a1/k）k（1ρ）≤σn（a,k）≤qAn（a）＋（1-q）Gn（a）, and q=n-k/n-1和p=n-k/kn-k were the best constants. By the compressed independent variables theorem, the optimal inequalities were established.