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

<p>In the present research, we estimate some approximation properties for the generalization of a sequence of positive linear operators considered by Holhoş [<xref ref-type="bibr" rid="j_gm-2022-0016_ref_006">6</xref>] with the following operators available in literature as special examples: Szàsz operator, Ismail-May operator associated with <italic>x</italic>(1 + <italic>x</italic>)<sup>2</sup>. We estimate its recurrence relation, moments and verify the same for its particular cases. Finally, we graphically compare the convergence of this new general operator for a continuous function, examine the convergence for each instance, and come to a conclusion regarding which scenario provides the best approximation.</p>
</abstract>

In the present research, we estimate some approximation properties for the generalization of a sequence of positive linear operators considered by Holhoş [6] with the following operators available in literature as special examples: Szàsz operator, Ismail-May operator associated with x(1 + x)2. We estimate its recurrence relation, moments and verify the same for its particular cases. Finally, we graphically compare the convergence of this new general operator for a continuous function, examine the convergence for each instance, and come to a conclusion regarding which scenario provides the best approximation.

Approximation properties of a discrete operator

General Mathematics

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

In the present research, we estimate some approximation properties for the generalization of a sequence of positive linear operators considered by Holhoş [6]...

Approximation properties of a discrete operator

Published Online: Nov 24, 2023

Page range: 63 - 72

Received: Oct 06, 2022

Accepted: Nov 20, 2022

DOI: https://doi.org/10.2478/gm-2022-0016

Keywords
Szàsz operator, Ismail-May operator, Convergence Estimates, Voronovskaya Theorem

© 2022 Anjali, published by Sciendo

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

Approximation properties of a discrete operator

Published Online: Nov 24, 2023

Page range: 63 - 72

Received: Oct 06, 2022

Accepted: Nov 20, 2022

DOI: https://doi.org/10.2478/gm-2022-0016

KeywordsSzàsz operator, Ismail-May operator, Convergence Estimates, Voronovskaya Theorem

© 2022 Anjali, published by Sciendo

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

Keywords
Szàsz operator, Ismail-May operator, Convergence Estimates, Voronovskaya Theorem