<abstract xmlns="http://www.w3.org/1999/xhtml"><p>On the last five decades the interest of the study of positive approximation processes have emerged with growing evidence. A special place is occupied by the in-depth study of classical operators. The most eloquent example is Bernstein operator which represents a permanent challenge for the researches in the mentioned field.</p><p>However, in this synthesis we focused on presenting a class of operators introduced by G.C. Jain in the 1970s that have long been in a shadowy cone. In recent years many papers have appeared about their properties and many generalizations have been analyzed. In our approach, there is no question of an exhaustive treatment, but only of collecting some published results that prove the importance of this class through the generous possibilities o ered by the approximation of signals from different function spaces.</p></abstract>

On the last five decades the interest of the study of positive approximation processes have emerged with growing evidence. A special place is occupied by the in-depth study of classical operators. The most eloquent example is Bernstein operator which represents a permanent challenge for the researches in the mentioned field.However, in this synthesis we focused on presenting a class of operators introduced by G.C. Jain in the 1970s that have long been in a shadowy cone. In recent years many papers have appeared about their properties and many generalizations have been analyzed. In our approach, there is no question of an exhaustive treatment, but only of collecting some published results that prove the importance of this class through the generous possibilities o ered by the approximation of signals from different function spaces.

A stop over Jain operators and their generalizations

Faculty of Mathematics and Computer Science

Annals of West University of Timisoara - Mathematics and Computer Science

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

{"article-title":"A stop over Jain operators and their generalizations"}

On the last five decades the interest of the study of positive approximation processes have emerged with growing evidence. A special place is occupied by the...

A stop over Jain operators and their generalizations

Published Online: Apr 30, 2020

Page range: 28 - 42

DOI: https://doi.org/10.2478/awutm-2018-0014

Keywords
Linear positive operator, Poisson distribution, Korovkin theorem, modulus of smoothness, weighted space, statistical convergence, Voronovskaja theorem

© 2018 Octavian Agratini, published by Sciendo

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

A stop over Jain operators and their generalizations

Published Online: Apr 30, 2020

Page range: 28 - 42

DOI: https://doi.org/10.2478/awutm-2018-0014

KeywordsLinear positive operator, Poisson distribution, Korovkin theorem, modulus of smoothness, weighted space, statistical convergence, Voronovskaja theorem

© 2018 Octavian Agratini, published by Sciendo

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

Keywords
Linear positive operator, Poisson distribution, Korovkin theorem, modulus of smoothness, weighted space, statistical convergence, Voronovskaja theorem