Singular approximation in polydiscs by summability process

Abstract

In this paper, 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 regular summability method (process) from the summability theory. We show that our results are non-trivial generalizations of the classical approximations. At the end, we display an application verifying the singular approximation via summation process, but not the usual sense.