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\"{o}rlund summability, complemented by illustrative examples. Leveraging this approach, we establish a new Korovkin-type theorem for a specific class of algebraic test functions, namely ۱, x and x^{۲}, within the Banach space \mathfrak{C}[۰,۱]. 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\"{o}rlund 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.

Keywords:

Statistical derivative , Deferred N&ouml , rlund mean Korovkin-type theorem , Bernstein polynomials , Rate of convergence