turkmath.org

In this talk, we approximate a continuous function in a polydisc by means of multivariate complex singular operators which preserve the analytic functions. In this singular approximation, we mainly use a general form of regular summability methods (process), which includes the well-known convergence methods, such as, the usual convergence by Cauchy, the arithmetic mean by Cesàro and the almost convergence by Lorentz. We also show that our results are non-trivial generalizations of the classical approximations. At the end of the talk, we display an application verifying the singular approximation via summation process, but not the usual sense.