Uniform Convergence of Double Fourier Series via (p,q)‐Deferred Cesàro Means and Its Applications

ABSTRACT In this article, we identify a notable limitation in the theory of summability for double Fourier series. Specifically, while the Fourier series of ‐periodic functions of two variables is uniformly convergent via the Cesàro mean, this convergence does not extend to arbitrary periodic functions of two variables. To address this issue, we introduce and study the concept of the deferred Cesàro mean based on ‐integers for the double Fourier series of arbitrary periodic functions. Moreover, we explore the behavior of our proposed method under both ordinary and statistical convergence. In this context, we establish two Korovkin‐type approximation theorems for trigonometric test functions in two variables. Finally, we present several examples with geometric illustrations to demonstrate the effectiveness of the proposed method and validate the results obtained in this work.