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

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{CMUC_2008__49_4_a4,
     author = {Rempulska, Lucyna and Tomczak, Karolina},
     title = {On approximation of functions by certain operators preserving $x^2$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {579--593},
     publisher = {mathdoc},
     volume = {49},
     number = {4},
     year = {2008},
     mrnumber = {2493939},
     zbl = {1212.41054},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2008__49_4_a4/}
}
TY  - JOUR
AU  - Rempulska, Lucyna
AU  - Tomczak, Karolina
TI  - On approximation of functions by certain operators preserving $x^2$
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2008
SP  - 579
EP  - 593
VL  - 49
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2008__49_4_a4/
LA  - en
ID  - CMUC_2008__49_4_a4
ER  - 
%0 Journal Article
%A Rempulska, Lucyna
%A Tomczak, Karolina
%T On approximation of functions by certain operators preserving $x^2$
%J Commentationes Mathematicae Universitatis Carolinae
%D 2008
%P 579-593
%V 49
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2008__49_4_a4/
%G en
%F CMUC_2008__49_4_a4
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/