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

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.