This note aims to highlight a general class of discrete linear and positive operators, focusing on some of their approximation properties. The construction includes a sequence of positive numbers ðknÞ, strictly decreasing. Imposing additional conditions on it, we set the convergence of the operators towards the identity operator and establish upper bounds for the error of approximation. A probabilistic approach is given. Also, in certain weighted spaces the study of its approximation properties is developed.


Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Abdulofizov generalization; Balazs-Szabados operator; Korovkin theorem; modulus of smoothness.

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O. Agratini, On a class of Bernstein-type rational functions, Numerical Functional Analysis and Optimization, 41 (2020) no. 4, pp. 483-494, https://doi.org/10.1080/01630563.2019.1664566


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