Izvorni znanstveni članak

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

Sažetak

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.

Ključne riječi

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

Hrčak ID:

53220

URI

https://hrcak.srce.hr/53220

Datum izdavanja:

10.6.2010.

Posjeta: 1.433 *