Korovkin-type Theorems via Statistical Derivatives of Deferred Nörlund Summability

This paper introduces and explores the concept of statistical derivatives within the framework of deferred N\"orlund summability, complemented by illustrative examples. Leveraging this approach, we establish a new Korovkin-type theorem for a specific class of algebraic test functions, namely 1, x and x^2, within the Banach space C0, 1. Our findings serve as a significant generalization of several classical and statistical Korovkin-type results in approximation theory. Furthermore, we examine the rate of convergence associated with statistical derivatives under deferred N\"orlund summability, providing insights into the effectiveness of this summability method. To validate our theoretical results, we present numerical examples alongside graphical visualizations created using MATLAB, offering a clearer perspective on the convergence behavior of the proposed operators.