修正q-Szász-Kantorovich算子逼近性质

Approximation Properties of the Modified q-Szász-Kantorovich Operator

Szász算子和Kantorovich算子的良好性质引起了学者的广泛关注,成为研究算子逼近问题的重要工具之一。为此,构造一类新的修正q-Szász-Kantorovich算子,利用原点矩估计式和中心矩估计式得到Voronovskaja型定理,根据K-泛函和光滑模的性质研究算子的局部逼近性质,并利用Lipschitz函数类的性质对算子进行点估计。

The good properties of the Szász operators and the Kantorovich operators have attracted the attention of the scholars, and become one of the important tools to study the approximation of the operators. Therefore a new kind of modified q-Szász-Kantorovich operators is constructed in the paper. The Voronovskaja theorem is obtained by the means of the moments’ and the central moments’ estimates. We also have studied the local approximation properties of operators according to the K-functional and the order of the modulus of continuity. Lastly we propose the point-wise estimate using the Lipschitz function.