On new Bézier bases with Schurer polynomials and corresponding results in approximation theory

Year 2020, Volume: 69 Issue: 1, 376 - 393, 30.06.2020

Faruk Özger

https://doi.org/10.31801/cfsuasmas.510382

Cited By: 21

Abstract

A new type Bézier bases with λ shape parameters have been defined <cite>ye</cite>. We slightly modify these bases to establish new Bézier bases with Schurer polynomials and λ shape parameters. We construct a new type Schurer operators via defined new Bézier-Schurer bases. Also, we study statistical convergence properties of these operators and obtain an estimate for the rate of weighted A-statistical convergence. Moreover, we prove two Voronovskaja-type theorems including a Voronovskaja-type approximation theorem using weighted A-statistical convergence.

Keywords

Bézier bases, shape parameter, statistical approximation, $ \lambda $-Schurer operators, weighted A-statistical Voronovskaja-type theorem

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