Statistical Riemann and Lebesgue integrability by deferred Cesàro and deferred Nörlund mean and Korovkin’s theorem

Abstract The current work focuses on statistical Riemann summability, statistical Riemann integrability, statistical Lebesgue summability, and statistical Lebesgue integrability using Deferred Cesàro and Deferred Nörlund means. First, we explore key theorems that connect these concepts, providing examples for illustration. In our newly established sequence spaces, we illustrate the application of Korovkin-type approximation theorems, supported by some examples of positive linear operators showcasing the significance of our results.