多元正系数代数多项式倒数对非负连续函数的逼近

APPROXIMATION OF NONNEGATIVECONTINUOUS FUNCTIONS BY RECIPROCALSOF MULTIVARIATE ALGEBRAIC POLYNOMIALSWITH POSITIVE COEFFICIENTS

设d≥1为正整数, S为Rd中的单纯形,C(S)为S上的连续函数类,f(x)∈C(S),f(x)≥0,f(?)0,则文中证明存在,绝对常数C>0使 这里 为单纯形S上的一阶Ditzian-Totik光滑模,

Let d ≥ 1 be a positive integer,S be the simplex in R , C(S) be the class of continuous functions defined on S, f(x) ∈C(5), f(x) ≥0, f(?) 0. It is proved in the present paper that there exists an algebraic polynomial and a constant C > 0 such that here, is the first order Ditzian-Totik's modulus of continuity denned on S and