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September 5, 2025

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

Key Points

Statistical Riemann and Lebesgue integrability is thoroughly explored using deferred means and key theorems.
Examples of positive linear operators show the significance of statistical summability in newly established sequence spaces.
Deferred Cesàro and Nörlund means facilitate the understanding of integrability with practical applications in approximation.
The findings emphasize the foundational relationships between statistical summability and integrability concepts.

Abstract

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.

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