<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We introduce a new generalization of the q-Bernstein operators involving (p, q)-integers, and we establish some direct approximation results. Further, we define the limit (p, q)-Bernstein operator, and we obtain its estimation for the rate of convergence. Finally, we introduce the (p, q)-Kantorovich type operators, and we give a quantitative estimation.</p></abstract>

We introduce a new generalization of the q-Bernstein operators involving (p, q)-integers, and we establish some direct approximation results. Further, we define the limit (p, q)-Bernstein operator, and we obtain its estimation for the rate of convergence. Finally, we introduce the (p, q)-Kantorovich type operators, and we give a quantitative estimation.

Approximation properties of (p, q)-Bernstein type operators

Department of Mathematics, Babeş-Bolyai University,

Acta Universitatis Sapientiae, Mathematica

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

{"article-title":"Approximation properties of (p, q)-Bernstein type operators"}

We introduce a new generalization of the q-Bernstein operators involving (p, q)-integers, and we establish some direct approximation results. Further, we...

Approximation properties of (p, q)-Bernstein type operators

Published Online: Jan 23, 2017

Page range: 222 - 232

Received: Apr 15, 2016

DOI: https://doi.org/10.1515/ausm-2016-0014

Keywords
(p, q)-integers, (p, q)-Bernstein operators, limit (p, q)-Bernstein operator, (p, q)-Kantorovich operators, rate of convergence, modulus of continuity

© 2016 Zoltán Finta, published by De Gruyter Open

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

Approximation properties of (p, q)-Bernstein type operators

Published Online: Jan 23, 2017

Page range: 222 - 232

Received: Apr 15, 2016

DOI: https://doi.org/10.1515/ausm-2016-0014

Keywords(p, q)-integers, (p, q)-Bernstein operators, limit (p, q)-Bernstein operator, (p, q)-Kantorovich operators, rate of convergence, modulus of continuity

© 2016 Zoltán Finta, published by De Gruyter Open

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

Keywords
(p, q)-integers, (p, q)-Bernstein operators, limit (p, q)-Bernstein operator, (p, q)-Kantorovich operators, rate of convergence, modulus of continuity