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On Szász-Mirakyan type operators preserving polynomials. (English) Zbl 1413.41033

Summary: In this paper, a modification of Szász-Mirakyan operators is studied [O. Agratini and S. Tarabie, “On approximating operators preserving certain polynomials”, Automat. Comput. Appl. Math. 17, 191–199 (2008)] which generalizes the Szász-Mirakyan operators with the property that the linear combination \(e_2+\alpha e_1\) of the Korovkin’s test functions \(e_1\) and \(e_2\) are reproduced for \(\alpha \geq 0\). After providing some computational results, shape preserving properties of mentioned operators are obtained. Moreover, some estimations for the rate of convergence of these operators by using different type modulus of continuity are shown. Furthermore, a Voronovskaya-type formula and an approximation result for derivative of operators are calculated.

MSC:

41A36 Approximation by positive operators
41A25 Rate of convergence, degree of approximation
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