# Approximation of continuous periodic functions of two variables via power series methods of summability

## TL;DR

This paper establishes a Korovkin type approximation theorem for continuous two-variable periodic functions using power series summability methods, demonstrating convergence of positive linear operators with an example involving double Fourier series.

## Contribution

It introduces a new approximation theorem for two-variable periodic functions using power series summability, extending Korovkin's classical results.

## Key findings

- Proves convergence of double sequences of positive linear operators.
- Provides an example with double Fourier series.
- Extends approximation theory to two-variable periodic functions.

## Abstract

We prove a Korovkin type approximation theorem via power series methods of summability for continuous $2\pi$-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.