Srivastava, H.M.Jena, Bidu BhusanPaikray, Susanta Kumar2022-11-162022-11-1620212021Srivastava, H. M., Jena, B. B., & Paikray, S. K. (2021). “Statistical Riemann and Lebesgue integrable sequence of functions with Korovkin-type approximation theorems.” Axioms, 10(3), 229. https://doi.org/10.3390/axioms10030229https://doi.org/10.3390/axioms10030229http://hdl.handle.net/1828/14476In this work we introduce and investigate the ideas of statistical Riemann integrability, statistical Riemann summability, statistical Lebesgue integrability and statistical Lebesgue summability via deferred weighted mean. We first establish some fundamental limit theorems connecting these beautiful and potentially useful notions. Furthermore, based upon our proposed techniques, we establish the Korovkin-type approximation theorems with algebraic test functions. Finally, we present two illustrative examples under the consideration of positive linear operators in association with the Bernstein polynomials to exhibit the effectiveness of our findings.enriemann integrallebesgue integralstatistical convergencedeferred weighted meanbanach spacepositive linear operatorsbernstein polynomialKorovkin-type approximation theoremsArticleDepartment of Mathematics and Statistics