某类凸函数的保凸逼近

CONVEX APPROXIMATION OF SOME KIND OF CONVEX FUNCTIONS

本文证明了当凸函数f(x)(∈C^2[0,1])满足ω型强凸性条件时,存在着凸的n阶代数多项式Pn(x),使得|f(x)-P_n(x)|≤Cn^(-2)ω(f″,1/n)

For convex function f(x)∈C^2[0,1], we prove that if f(x) satisfies the sLrong convex condition of ω-type, then there exist convex algebraic polynomials P_n(x) of degree such that |f(x)-P_n(x)|≤Cn^(-2)ω(f″,_n^1)