Approximation by complex Bernstein–Schurer and Kantorovich–Schurer polynomials in compact disks

In this paper, the order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex Bernstein–Schurer and Kantorovich–Schurer polynomials attached to analytic functions on compact disks are obtained. In this way, we put in evidence the overconvergence phenomenon for the Bernstein–Schurer polynomials, namely the extensions of approximation properties (with quantitative estimates) from real intervals to compact disks in the complex plane.