The Approximation For Linear Combination Of The Two-dimensional Bernstein Operators

The aim of this paper is to discuss the approximation property of linear combinations oftwo-dimensional Bernstein operators B_n,r(f,x,y)defined on a simplex．Firstly we discusssome different derivative expressions of B_n(f,x,y)．Secondly we give the expression andthe upper estimate of B_n,r((·-x)^s(·-y)^t,x,y)．Finally,with the help of a new K-fuctionaland the interpolation space(C,A)αgiven by the K-fuctional,we obtain the direct andinverse theorems on approximation for operator B_n,r(f,x,y)．From these results we canfind that operator B_n,r(f,x,y)accelerate covergence of operator B_n(f,x,y)．...