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由幂函数的凹凸性可以得到下面两个不等式(权方和不等式的推广):若00,p_i>0 (i=1,2,…,m)且sum from i=1 to m p_i=1,则sum from i=1 to m p_ia_i~n≤(sum from i=1 to m p_ia_i)~n (1)若n>1或n<0,a_i>0,p_i>0(i=1,2,…,m)且sum from i=1 to m p_i=1,则sum from i=1 to m p_ia_i~n≥(sum from i=1 to m p_ia_i)~n.(2)本文利用上述两个不等式探求一类函数的最
The following two inequalities (generalizations of weights and inequalities) can be obtained from the convexity and concavity of the power function: if 0 0, p_i> 0 (i = 1,2, ..., m) = 1 to m p_i = 1, then sum from i = 1 to m p_ia_i ~ n ≤ (sum from i = 1 to m p_ia_i) ~ n If n> 1 or n <0, a_i> 0, p_i> Sum from i = 1 to m p_ia_i to n≥ (sum from i = 1 to m p_ia_i) to n (0 (i = 1, 2, ..., m) and sum from i = 1 to m p_i = 2) This paper uses the above two inequalities to find the most of a class of functions