<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we obtain estimations of the errors in approximation by positive linear operators which fix certain functions. We use both the first and the second order classical moduli of smoothness and a generalized modulus of continuity of order two. Some applications involving Bernstein type operators, Kantorovich type operators and genuine Bernstein-Durrmeyer type operators are presented.</p></abstract>

In this paper we obtain estimations of the errors in approximation by positive linear operators which fix certain functions. We use both the first and the second order classical moduli of smoothness and a generalized modulus of continuity of order two. Some applications involving Bernstein type operators, Kantorovich type operators and genuine Bernstein-Durrmeyer type operators are presented.

Quantitative results for positive linear operators which preserve certain functions

Faculty of Automatics and Computer Science, Department of Mathematics

General Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper we obtain estimations of the errors in approximation by positive linear operators which fix certain functions. We use both the first and the...

Quantitative results for positive linear operators which preserve certain functions

Published Online: Mar 20, 2020

Page range: 85 - 95

Received: Oct 24, 2019

Accepted: Nov 18, 2019

DOI: https://doi.org/10.2478/gm-2019-0017

Keywords
positive linear operators, errors estimations, classical moduli of smoothness, generalized modulus of continuity, Kantorovich type operators, genuine Bernstein-Durrmeyer type operators

© 2019 Marius-Mihai Birou, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Quantitative results for positive linear operators which preserve certain functions

Published Online: Mar 20, 2020

Page range: 85 - 95

Received: Oct 24, 2019

Accepted: Nov 18, 2019

DOI: https://doi.org/10.2478/gm-2019-0017

Keywordspositive linear operators, errors estimations, classical moduli of smoothness, generalized modulus of continuity, Kantorovich type operators, genuine Bernstein-Durrmeyer type operators

© 2019 Marius-Mihai Birou, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
positive linear operators, errors estimations, classical moduli of smoothness, generalized modulus of continuity, Kantorovich type operators, genuine Bernstein-Durrmeyer type operators