Approximation by Bernstein-Durrmeyer-type operators in compact disks - Mahmudov, N. I. (Pergamon-Elsevier Science Ltd, 2011)
In this paper, the order of simultaneous approximation and Voronovskaja-type theorems with quantitative estimate for complex Bernstein-Durrmeyer-type polynomials attached to analytic functions on compact disks are obtained. Our results show that extension of the complex Bernstein-Durrmeyer-type polynomials from real intervals to compact disks in the complex plane extends approximation properties. (c) 2011 Elsevier Ltd. All rights reserved.
Keywords: Complex Bernstein-Durrmeyer-type polynomials; Simultaneous approximation; Voronovskaja-type result