On Szász-Mirakyan type operators preserving polynomials

Ovgu Gurel Yilmaz; Ali Aral; Fatma Taşdelen Yeşildal

doi:10.33993/jnaat461-1087

Authors

Ovgu Gurel Yilmaz University of Ankara, Department of Mathematics, Turkey
Ali Aral University of Kırıkkale, Department of Mathematics, Turkey
Fatma Taşdelen Yeşildal University of Ankara, Department of Mathematics, Turkey

DOI:

https://doi.org/10.33993/jnaat461-1087

Keywords:

Szász-Mirakyan operators, shape preserving properties, Voronovskaya-type theorem., modified operator

Abstract views: 503

Abstract

In this paper, a modification of Szász-Mirakyan operators is studied [1] 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. Finally, some graphics which are based on our main results are shown.

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Author Biographies

Ovgu Gurel Yilmaz, University of Ankara, Department of Mathematics, Turkey

MATHS DEPARTMENT

Ali Aral, University of Kırıkkale, Department of Mathematics, Turkey

MATS DEPARTMENT

Fatma Taşdelen Yeşildal, University of Ankara, Department of Mathematics, Turkey

MATHS DEPARTMENT

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