Asymptotic formulae for modified Bernstein operators based on regular summability methods

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 special cases of our results including the methods of Cesàro 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 asymptotic formula
• regular summability methods
• matrix methods
• power series methods

References

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