Statistical Riemann and Lebesgue integrable sequence of functions with Korovkin-type approximation theorems
Date
2021
Authors
Srivastava, H.M.
Jena, Bidu Bhusan
Paikray, Susanta Kumar
Journal Title
Journal ISSN
Volume Title
Publisher
Axioms
Abstract
In 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.
Description
Keywords
riemann integral, lebesgue integral, statistical convergence, deferred weighted mean, banach space, positive linear operators, bernstein polynomial, Korovkin-type approximation theorems
Citation
Srivastava, 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/axioms10030229