On wavelet type generalized Bézier operators
Harun Karslı · Mathematical Foundations of Computing · 2022
This paper deals with construction and studying wavelet type generalized Bézier operators by using the compactly supported Daubechies wavelets of the given function $ f $. The basis used in this construction are the wavelet expansion of the function $ f $ instead of its rational sampling values $ f\left( \frac{k}{n}\right) $. By using the Chanturiya modulus of variation we estimate the rate of pointwise convergence of $ \left( WB_{n, \alpha }f\right) (x)\ $at those $ x>0 $ at which the one-sided limits $ f(x+) $, $ f(x-) $ exist.Clearly our wavelet type operators contain at least classical version, Durrmeyer and the Kantorovich form of the generalized Bézier operators and hence our results extend some of the previous results on generalized B ézier operators, such as [1], [11] and [12].