# Modified double Szász-Mirakjan operators preserving $x^{2} y^{2}$

Modified double Szász-Mirakjan operators preserving $x^{2} y^{2}$ - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Mathematical Communications, Vol.15 No.1 June 2010. -

In this paper, we introduce a modification of the Sz\-{a}sz-Mirakjan type operators of two variables which preserve $f {0}\left x,y ight =1$ and $% f {3}\left x,y ight =x^{2}+y^{2}.$ We prove that this type of operators enables a better error estimation on the interval $\left 0,\infty ight \times \left 0,\infty ight$ than the classical Sz\-{a}sz-Mirakjan type operators of two variables. Moreover, we prove a Voronovskaya-type theorem

and some differential properties for derivatives of these modified

operators. Finally, we also study statistical convergence of the sequence of modified Sz\-{a}sz-Mirakjan type operators.

Szász-Mirakjan type operators; A-statistical convergence; the Korovkin-type approximation theorem; modulus of continuity

Autor: Fadime Dirik - ; Department of Mathematics, Faculty of Arts and Sciences, Sinop University, Sinop, Turkey Kamil Demirci - ; Depar

Fuente: http://hrcak.srce.hr/

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