On wavelet type Bernstein operators

Abstract

This paper deals with construction and studying wavelet type Bernstein operators by using the compactly supported Daubechies wavelets of the given function $f$. The basis used in this construction is the wavelet expansion of the function $f$ instead of its rational sampling values $f\big( \frac{k}{n}\big)$. After that, we investigate some properties of these operators in some function spaces.

Keywords

• bernstein polynomial
• interpolation
• wavelet
• compactly supported daubechies wavelet
• approximation