Geodesic
On approximation of functions by certain operators preserving $x^2$
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 4, pp. 579-593

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In this paper we extend the Duman-King idea of approximation of functions by positive linear operators preserving $e_k (x)=x^k$, $k=0,2$. Using a modification of certain operators $L_n$ preserving $e_0$ and $e_1$, we introduce operators $L_n^*$ which preserve $e_0$ and $e_2$ and next we define operators $L_{n;r}^{*}$ for $r$-times differentiable functions. We show that $L_n^*$ and $L_{n;r}^{*}$ have better approximation properties than $L_n$ and $L_{n;r}$.
Classification : 41A25, 41A36
Keywords: positive linear operators; polynomial weighted space; degree of approximation 
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     title = {On approximation of functions by certain operators preserving $x^2$},
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Rempulska, Lucyna; Tomczak, Karolina. On approximation of functions by certain operators preserving $x^2$. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 4, pp. 579-593. http://geodesic.mathdoc.fr/item/CMUC_2008__49_4_a4/