Approximation by Complex Bernstein-Durrmeyer Polynomials in Compact Disks


In this paper, the order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for complex Bernstein-Durrmeyer polynomials attached to analytic functions on compact disks are obtained. In this way, we put in evidence the overconvergence phenomenon for Bernstein-Durrmeyer polynomials, namely the extensions of approximation properties (with quantitative estimates) from real intervals to compact disks in the complex plane. © 2010 Birkhäuser / Springer Basel AG.

Publication Title

Mediterranean Journal of Mathematics