<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper we introduce a novel extension of generalized Bézier operators by replacing the sample values <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2022-0010_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mfrac><mi>k</mi><mi>n</mi></mfrac></mrow><mo>)</mo></mrow></mrow></math>
<tex-math>f\left({{k\overn}}\right)</tex-math>
</alternatives>
</inline-formula> with the wavelet expansion of the function <italic>f. </italic>Using the compactly supported Daubechies wavelets, we construct a wavelet type extension of the generalized Bézier operators defined by Gupta [<xref ref-type="bibr" rid="j_gm-2022-0010_ref_007">7</xref>]. Moreover, we investigate some properties of these operators in some function spaces.</p>
</abstract>

In this paper we introduce a novel extension of generalized Bézier operators by replacing the sample values 


f(kn)
f\left({{k\overn}}\right)

 with the wavelet expansion of the function f. Using the compactly supported Daubechies wavelets, we construct a wavelet type extension of the generalized Bézier operators defined by Gupta [7]. Moreover, we investigate some properties of these operators in some function spaces.

Extension of the generalized Bézier operators by wavelets

Bolu Abant Izzet Baysal University Faculty of Science and Arts

General Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this paper we introduce a novel extension of generalized Bézier operators by replacing the sample values 


f(kn)
f\left({{k\overn}}\right)

 with the...

Extension of the generalized Bézier operators by wavelets

Published Online: Nov 24, 2023

Page range: 3 - 15

Received: Oct 07, 2022

Accepted: Dec 10, 2022

DOI: https://doi.org/10.2478/gm-2022-0010

Keywords
Bézier basis, wavelets, compactly supported Daubechies wavelets, approximation

© 2022 Harun Karsli, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Extension of the generalized Bézier operators by wavelets

Published Online: Nov 24, 2023

Page range: 3 - 15

Received: Oct 07, 2022

Accepted: Dec 10, 2022

DOI: https://doi.org/10.2478/gm-2022-0010

KeywordsBézier basis, wavelets, compactly supported Daubechies wavelets, approximation

© 2022 Harun Karsli, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Bézier basis, wavelets, compactly supported Daubechies wavelets, approximation