Asymptotic Formulae for Modified Bernstein Operators based on Regular Summability Methods

Year 2025, Early Access, 1 - 14

Meryem Ece Alemdar , Oktay Duman

https://doi.org/10.15672/hujms.1486862

Abstract

In this paper, we get new Voronovskaja-type asymptotic formulae for modified Bernstein operators by using regular summability methods. We also display some significant applications of our results including the methods of Cesaro summability, Riesz summability, Abel summability and Borel summability. At the end, we also discuss the similar results for the Kantorovich version of the operators.

Keywords

Bernstein polynomials, Bernstein-Kantorovich polynomials, Voronovskaja-type asymtotic formula, regular summability methods, matrix methods, power series methods

References

• [1] M. E. Alemdar and O. Duman, General summability methods in the approximation by Bernstein-Chlodovsky operators, Numer. Funct. Anal. Optim. 42 (5), 497–509, 2021