Statistical Riemann and Lebesgue Integrable Sequence of Functions with Korovkin-Type Approximation Theorems

In this work we introduce and investigate the ideas of statistical Riemann integrability, summability, Lebesgue integrability summability via deferred weighted mean. We first establish some fundamental limit theorems connecting these beautiful potentially useful notions. Furthermore, based upon our proposed techniques, Korovkin-type approximation with algebraic test functions. Finally, present two illustrative examples under consideration positive linear operators in association Bernstein polynomials to exhibit effectiveness findings.