Approximation of Continuous Periodic Functions of Two Variables via Power Series Methods of Summability

Abstract

We prove a Korovkin type approximation theorem via power series methods of summability for continuous 2π-periodic functions of two variables and verify the convergence of approximating double sequences of positive linear operators by using modulus of continuity. An example concerning double Fourier series is also constructed to illustrate the obtained results.

A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices

“…r,s,κ,β via Power Series Method Korovkin type approximation theory by power series method have been studied in several function spaces by many researchers (see [44][45][46][47]). In this section, certain Korovkin type theorems for linear positive operators, and specifically for bivariate Bernstein-Kantorovich type operators on extended domain with reparametrized knots are proven by the power series method.…”