Approximation and geometric properties of complex Favard–Szász–Mirakjan operators in compact disks

In this paper, first we obtain quantitative estimates of the convergence and of the Voronovskaja’s theorem in compact disks, for complex Favard–Szász–Mirakjan operators attached to analytic functions satisfying some suitable exponential-type growth condition. Then, we prove that beginning with an index, these operators preserve the starlikeness, convexity and spirallikeness in the unit disk.