二元函数空间上指数型算子的整体逼近定理

Global Approximation Theorems for Some Exponential-type Operators on Space of Two-variate Function

引入二元函数空间上的指数型算子,并建立其整体逼近的等价定理。

continuous on D}exponential-type operators are given by La1,ax (f;x1,x2)== W(n1, n2;x1,x2;x3, u2)f(u1,u2)du1du2,(n1,n2∈N), If φa (xa)(x=1,2) has no double zero and satisfieswhere α1=min(x1,x2 +φ', (x3)/n3),βn= max(x1,x2 +φ'.(xa)/nb) ,M/ is an absolute constant indepent of ni and X1, then the following theorem is obetained.Theorem Let φ1(x1)(i= 1,2) satisfy the above condition. Then for f∈C(D),ω2(f,h)<+∞ (0<k<h0<+∞)and 0<α<2, the following statements are equivalent.