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The first aim of this paper is to prove a Gr\"uss-Voronovskaya estimate forBernstein and for a class of Bernstein-Durrmeyer polynomials on $[0, 1]$. Then,Gr\"uss and Gr\"uss-Voronovskaya estimates for their corresponding operators ofcomplex variable on compact disks are obtained. Finally, the results areextended to Bernstein-Faber polynomials attached to compact sets in the complexplane.

Gr\"uss and Gr\"uss-Voronovskaya-type estimates for some Bernstein-type polynomials of real and complex variables