Approximation by complex Favard-Szász-Mirakjan-Stancu operators in compact disks

Purpose: The purpose of the present paper is to study the Stancu-type generalization of complexFavard-Szász-Mirakjan operators and establish some approximation results in complex domain.Methods: It is observed that the complex Favard-Szász-Mirakjan-Stancu operators can be written in the form of divided differences. Thus, it is possible to study such operators in complex domain. We use analytical method to obtain our results.Results: We have estimated the order of simultaneous approximation, Voronovskaja-type results with quantitative estimates for the complex Favard-Szász-Mirakjan-Stancu operators attached to analytic functions on compact disks.Also, some estimates on the rate of convergence are given.Conclusions: The results proposed here are new and have better rate of convergence.