【摘要】 著名的Jensen不等式可表述为:设函数f:I→R(I为给定的区间)为凸函数,如果x1,x2,…,xN∈I,那么有不等式:N-1.∑iN=1f(xi)≥f N-1.∑iN=1xi.借助于积和式及数学归纳法,将这个不等式推广到涉及m次齐次对称多项式的情形,由此获得了一个有趣的推论.更多还原

【Abstract】 The well-known inequality states that: let f:I→R be a convex function,where I is an interval,if x1,x2,…,xN∈I,then N-1·∑Ni=1f(xi)≥fN-1·∑Ni=1xi.By means of permanent and mathematical induction,this paper generalizs this inequality to the case involving homogeneous and symmetric polynomials of degree m.Thus,an interesting corollary are obtained.更多还原