【摘要】 <正> 1.引言 用△_k是表示R^k中的单纯形:△_k={X=（x₁,x₂,…,x_k）∈R^k|x_i≥0,i=1,2,…,k;sum from i=1 to k（x_i）≤1};C（△_k）表示定义在△_k上的连续函数的全体.记||f||=||f||_△k:=sup|f（X）|,ω（f,t）:=sup |f（X）-f（Y）|。连续函数ω（t）,t∈[0,+∞)称为更多还原

【Abstract】 This paper gives several theorems on Bernstein polynomials approximation forcontinuous convex functions defined on the k-dimensional simplex. These theoremsshow that the orders of the approximation are （in the general case） better thanω(f,1/n^1/2). Also our results give a negative answer to G. G. Lorentz’s conjectureproposed in [4].更多还原