King type modification of q -Bernstein-Schurer operators

Mei-Ying Ren; Xiao-Ming Zeng

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 3, page 805-817
  • ISSN: 0011-4642

Abstract

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Very recently the q -Bernstein-Schurer operators which reproduce only constant function were introduced and studied by C. V. Muraru (2011). Inspired by J. P. King, Positive linear operators which preserve x 2 (2003), in this paper we modify q -Bernstein-Schurer operators to King type modification of q -Bernstein-Schurer operators, so that these operators reproduce constant as well as quadratic test functions x 2 and study the approximation properties of these operators. We establish a convergence theorem of Korovkin type. We also get some estimations for the rate of convergence of these operators by using modulus of continuity. Furthermore, we give a Voronovskaja-type asymptotic formula for these operators.

How to cite

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Ren, Mei-Ying, and Zeng, Xiao-Ming. "King type modification of $q$-Bernstein-Schurer operators." Czechoslovak Mathematical Journal 63.3 (2013): 805-817. <http://eudml.org/doc/260710>.

@article{Ren2013,
abstract = {Very recently the $q$-Bernstein-Schurer operators which reproduce only constant function were introduced and studied by C. V. Muraru (2011). Inspired by J. P. King, Positive linear operators which preserve $x^\{2\}$ (2003), in this paper we modify $q$-Bernstein-Schurer operators to King type modification of $q$-Bernstein-Schurer operators, so that these operators reproduce constant as well as quadratic test functions $x^\{2\}$ and study the approximation properties of these operators. We establish a convergence theorem of Korovkin type. We also get some estimations for the rate of convergence of these operators by using modulus of continuity. Furthermore, we give a Voronovskaja-type asymptotic formula for these operators.},
author = {Ren, Mei-Ying, Zeng, Xiao-Ming},
journal = {Czechoslovak Mathematical Journal},
keywords = {King type operator; $q$-Bernstein-Schurer operator; Korovich type approximation theorem; rate of convergence; Voronovskaja-type result; modulus of continuity; King-type operator; -Bernstein-Schurer operator; Korovich-type approximation theorem; Voronovskaja-type result; modulus of continuity},
language = {eng},
number = {3},
pages = {805-817},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {King type modification of $q$-Bernstein-Schurer operators},
url = {http://eudml.org/doc/260710},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Ren, Mei-Ying
AU - Zeng, Xiao-Ming
TI - King type modification of $q$-Bernstein-Schurer operators
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 3
SP - 805
EP - 817
AB - Very recently the $q$-Bernstein-Schurer operators which reproduce only constant function were introduced and studied by C. V. Muraru (2011). Inspired by J. P. King, Positive linear operators which preserve $x^{2}$ (2003), in this paper we modify $q$-Bernstein-Schurer operators to King type modification of $q$-Bernstein-Schurer operators, so that these operators reproduce constant as well as quadratic test functions $x^{2}$ and study the approximation properties of these operators. We establish a convergence theorem of Korovkin type. We also get some estimations for the rate of convergence of these operators by using modulus of continuity. Furthermore, we give a Voronovskaja-type asymptotic formula for these operators.
LA - eng
KW - King type operator; $q$-Bernstein-Schurer operator; Korovich type approximation theorem; rate of convergence; Voronovskaja-type result; modulus of continuity; King-type operator; -Bernstein-Schurer operator; Korovich-type approximation theorem; Voronovskaja-type result; modulus of continuity
UR - http://eudml.org/doc/260710
ER -

References

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