Statistical approximation to Bogel-type continuous and periodic functions

Abstract

In this paper, considering A-statistical convergence instead of Pringsheim's sense for double sequences, we prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on the space of all real valued Bogel-type continuous and periodic functions on the whole real two-dimensional space. A strong application is also presented. Furthermore, we obtain some rates of A-statistical convergence in our approximation.