Approximation Properties of the Blending-Type Bernstein–Durrmeyer Operators

oleh: Yu-Jie Liu, Wen-Tao Cheng, Wen-Hui Zhang, Pei-Xin Ye

Format: Article
Diterbitkan: MDPI AG 2022-12-01

Deskripsi

We construct the blending-type modified Bernstein–Durrmeyer operators and investigate their approximation properties. First, we derive the Voronovskaya-type asymptotic theorem for this type of operator. Then, the local and global approximation theorems are obtained by using the classical modulus of continuity and <i>K</i>-functional. Finally, we derive the rate of convergence for functions with a derivative of bounded variation. The results show that the new operators have good approximation properties.