Korovkin-Type Theorems for Positive Linear Operators Based on the Statistical Derivative of Deferred Cesàro Summability

In this paper, we introduce and investigate the concept of statistical derivatives within the framework of the deferred Cesàro summability technique, supported by illustrative examples. Using this approach, we establish a novel Korovkin-type theorem for a specific set of exponential test functions, namely 1, e−υ and e−2υ, which are defined on the Banach space C[0,∞). Our results significantly extend several well-known Korovkin-type theorems. Additionally, we analyze the rate of convergence associated with the statistical derivatives under deferred Cesàro summability. To support our theoretical findings, we provide compelling numerical examples, followed by graphical representations generated using MATLAB software, to visually illustrate and enhance the understanding of the convergence behavior of the operators.