On approximation of functions by certain operators preserving x 2

Lucyna Rempulska; Karolina Tomczak

Commentationes Mathematicae Universitatis Carolinae (2008)

  • Volume: 49, Issue: 4, page 579-593
  • ISSN: 0010-2628

Abstract

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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 .

How to cite

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Rempulska, Lucyna, and Tomczak, Karolina. "On approximation of functions by certain operators preserving $x^2$." Commentationes Mathematicae Universitatis Carolinae 49.4 (2008): 579-593. <http://eudml.org/doc/250487>.

@article{Rempulska2008,
abstract = {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 $L_\{n;r\}$.},
author = {Rempulska, Lucyna, Tomczak, Karolina},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {positive linear operators; polynomial weighted space; degree of approximation; positive linear operators; polynomial weighted space; degree of approximation},
language = {eng},
number = {4},
pages = {579-593},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On approximation of functions by certain operators preserving $x^2$},
url = {http://eudml.org/doc/250487},
volume = {49},
year = {2008},
}

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
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 4
SP - 579
EP - 593
AB - 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 $L_{n;r}$.
LA - eng
KW - positive linear operators; polynomial weighted space; degree of approximation; positive linear operators; polynomial weighted space; degree of approximation
UR - http://eudml.org/doc/250487
ER -

References

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  12. Rempulska L., Skorupka M., 10.1080/10652460701510527, Integral Transforms Spec. Funct. 18 9-10 (2007), 653-662. (2007) Zbl1148.41025MR2356794DOI10.1080/10652460701510527
  13. Rempulska L., Skorupka M., On approximation by Post-Widder and Stancu operators preserving x 2 , Kyung. Math. J., to appear. MR2527373
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