三角域上的二元Stancu算子

TWO DIMENTIONAL STANCU OPERATORS ON THE TRIANGLE

构造了三角形区域上一种新的二元Ｓｔａｎｃｕ型算子。

A two dimentional Stancu operators on the triangle s={(x,y)|0≤y≤x≤1} is constructed:S n,α (f;x,y)=n≥k≥l≥0P n,k,l (x,y,α)fkn,lnwhereP n,k,l (x,y,α)=1 (-n,-α) C k-l nC l n(x-y) (k-l,-α) (1-x+y) (n-k+l,-α) ×y (l,-α) (1-y) (n-l,-α) , f(x,y)∈C(s)hereu (n,h) =u(u-h)(u-2h)…(u-(n-1)h), u (-n,h) =[u (n,h) ] -1 . The approximation properties of the operators S n,α (f;x,y) and the limit of their iterates are discussed and follow theorems: Theorem 1 Let f(x,y)∈C(s),0≤α=α(n)→0 (n→∞), then the operators S n,α (f;x,y) converge uniformly to f(x,y) on s. Theorem4 For fixed n∈ N we have  lim k→∞[KG*4〗S (k) n,α (f;x,y)=f(0,0)+(f(1,0)-f(0,0))x+(f(1,1) -(f(1,0))y+(f(0,0)-f(1,0)-f(1,1))y(x-y) have been obtained. Here the iterates S (k) n,α (f) is defined as followingS (1) n,α (f)=S n,α (f) S k+1 n,α (f)=S n,α (S (k) n,α (f)) k=1,2,….