MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Szász-Mirakjan type operators of two variables providing a better estimation on $[0,1]\times[0,1]$
Fadime Dirik and Kamil Demirci

Abstract

This paper deals with a modification of the classical Szász-Mirakjan type operators of two variables. It introduces a new sequence of non-polynomial linear operators which hold fixed the polynomials $x^{2}+\alpha x$ and $y^{2}+\beta y$ with $\alpha ,\beta \in [0,\infty)$ and we study the convergence properties of the new approximation process. Also, we compare it with Szász-Mirakjan type operators and show an improvement of the error of convergence in $[0,1] \times [0,1]$. Finally, we study statistical convergence of this modification.

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Keywords: Szász-Mirakjan type operators, $A$-statistical convergence for double sequences, Korovkin-type approximation theorem, modulus of contiunity.

MSC: 41A25, 41A36

Pages:  59--66     

Volume  63 ,  Issue  1 ,  2011