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 offered by the approximation of signals from different function spaces.


Octavian Agratini
Babes-Bolyai University, Faculty of Mathematics and Computer Science, Romania,
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy


Linear positive operator; Poisson distribution; Korovkin theorem; modulus of smoothness; weighted space; statistical convergence; Voronovskaja theorem.


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O. Agratini, A stop over Jain operators and their generalizations, Analele Universitatii de Vest, Timisoara Seria Matematica – Informatica, 56 (2018) no. 2, 28– 42.
doi: 10.2478/awutm-2018-0014

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