Asymptotic Properties of Bernstein-Durrmeyer Operators

作者：Xu, Xiao-Wei^*; Zeng, Xiao-Ming^*

来源：Results in Mathematics, 2016, 69(3-4): 345-357.

DOI：10.1007/s00025-015-0482-y

• Bernstein-Durrmeyer operators
• Szasz-Durrmeyer operator
• Operator semigroups
• Rates of convergence
• Asymptotic expansion

It is known that Szasz-Durrmeyer operator is the limit, in an appropriate sense, of Bernstein-Durrmeyer operators. In this paper, we adopt a new technique that comes from the representation of operator semigroups to study the approximation issue as mentioned above. We provide some new results on approximating Szasz-Durrmeyer operator by Bernstein-Durrmeyer operators. Our results improve the corresponding results of Adell and De La Cal (Comput Math Appl 30:1-14, 1995).

• 出版日期2016-6
• 单位厦门大学