Some Korovkin-type approximation theorems associated with a certain deferred weighted statistical Riemann-integrable sequence of functions
Date
2022
Authors
Srivastava, H.M.
Jena, Bidu Bhusan
Paikray, Susanta Kumar
Journal Title
Journal ISSN
Volume Title
Publisher
Axioms
Abstract
Here, in this article, we introduce and systematically investigate the ideas of deferred
weighted statistical Riemann integrability and statistical deferred weighted Riemann summability for
sequences of functions. We begin by proving an inclusion theorem that establishes a relation between
these two potentially useful concepts. We also state and prove two Korovkin-type approximation
theorems involving algebraic test functions by using our proposed concepts and methodologies.
Furthermore, in order to demonstrate the usefulness of our findings, we consider an illustrative
example involving a sequence of positive linear operators in conjunction with the familiar Bernstein
polynomials. Finally, in the concluding section, we propose some directions for future research
on this topic, which are based upon the core concept of statistical Lebesgue-measurable sequences
of functions.
Description
Keywords
Riemann and Lebesgue integrals, statistical Riemann and Lebesgue integral, deferred weighted Riemann summability, Banach space, Bernstein polynomials, positive linear operators, Korovkin-type approximation theorems, Lebesgue-measurable sequences of functions
Citation
Srivastava, H., Jena, B., & Paikray, S. (2022). “Some Korovkin-type approximation theorems associated with a certain deferred weighted statistical Riemann-integrable sequence of functions.” Axioms, 11(3), 128. https://doi.org/10.3390/axioms11030128