Bernstein型算子线性组合加Jacobi权逼近及高阶导数的等价定理

Equivalent Approximation Theorems with Jacobi Weight for Combinations and Higher Derivatives of Bernstein Operators

本文利用加权Ditzian-Totik光滑模证明Bernstein型算子的线性组合加权逼近阶估计和等价定理;同时,研究加Jacobi权下Benstein型算子的高阶导数与所逼近函数光滑性之间的关系.

Using the Ditzian-Totik moduli of smoothness equivalent approximation theorem with Jacobi weight for combinations of Bernstein operators is established in the paper.And the relation between higher derivatives of the operators and the smoothness of functions to be approximated is also obtained in the paper.