Original scientific paper
Modified double Szász-Mirakjan operators preserving $x^{2}+y^{2}$
Fadime Dirik
; Department of Mathematics, Faculty of Arts and Sciences, Sinop University, Sinop, Turkey
Kamil Demirci
; Department of Mathematics, Faculty of Arts and Sciences, Sinop University, Sinop, Turkey
Abstract
In this paper, we introduce a modification of the Sz\'{a}sz-Mirakjan type operators of two variables which preserve $f_{0}\left( x,y\right) =1$ and $% f_{3}\left( x,y\right) =x^{2}+y^{2}.$ We prove that this type of operators enables a better error estimation on the interval $\left[ 0,\infty \right) \times \left[ 0,\infty \right) $ 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.
Keywords
Szász-Mirakjan type operators; A-statistical convergence; the Korovkin-type approximation theorem; modulus of continuity
Hrčak ID:
53220
URI
Publication date:
10.6.2010.
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