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

<p>In this paper we shall introduce a new type of Bernstein Durrmeyer operators which are not positive on the entire interval [0, 1]. For these operators we will study the uniform convergence on all continuous functions on [0, 1] as well as a result given in terms of modulus of continuity <italic>ω</italic>(<italic>f, δ</italic>). A Voronovskaja type theorem will be proved as well.</p>
</abstract>

In this paper we shall introduce a new type of Bernstein Durrmeyer operators which are not positive on the entire interval [0, 1]. For these operators we will study the uniform convergence on all continuous functions on [0, 1] as well as a result given in terms of modulus of continuity ω(f, δ). A Voronovskaja type theorem will be proved as well.

On approximation properties of some non-positive Bernstein-Durrmeyer type operators

Department of Mathematics and Computer Science

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

In this paper we shall introduce a new type of Bernstein Durrmeyer operators which are not positive on the entire interval [0, 1]. For these operators we will...

On approximation properties of some non-positive Bernstein-Durrmeyer type operators

Published Online: Feb 04, 2023

Page range: 251 - 269

Received: Mar 19, 2022

Accepted: Jul 25, 2022

DOI: https://doi.org/10.2478/auom-2023-0014

Keywords
Linear operators, non-positive operators, approximation by operators, quantitative results, Bernstein-Durrmeyer type operators

© 2023 Bianca Ioana Vasian, published by Sciendo

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

On approximation properties of some non-positive Bernstein-Durrmeyer type operators

Published Online: Feb 04, 2023

Page range: 251 - 269

Received: Mar 19, 2022

Accepted: Jul 25, 2022

DOI: https://doi.org/10.2478/auom-2023-0014

KeywordsLinear operators, non-positive operators, approximation by operators, quantitative results, Bernstein-Durrmeyer type operators

© 2023 Bianca Ioana Vasian, published by Sciendo

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

Keywords
Linear operators, non-positive operators, approximation by operators, quantitative results, Bernstein-Durrmeyer type operators