Grüss and Grüss-Voronovskaya-type estimates for some Bernstein-type polynomials of real and complex variables

Abstract

The first aim of this paper is to prove a Grüss-Voronovskaya estimate for Bernstein and for a class of Bernstein-Durrmeyer polynomials on $[0,1]$. Then, Grüss and Grüss-Voronovskaya estimates for their corresponding operators of complex variable on compact disks are obtained. Finally, the results are extended to Bernstein-Faber polynomials attached to compact sets in the complex plane.

Cited by in corpus (1)

• Semi-discrete Gruss-Voronovskaya-type and Gruss-type estimates for Bernstein-Kantorovich polynomials