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 $f_0(x,y)=1$ and $$ We prove that this type of operators enables a better error estimation on the interval $[0,\mathrm{\infty })\times [0,\mathrm{\infty })$ 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

https://hrcak.srce.hr/53220

Publication date:

10.6.2010.

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