King type modification of $q$-Bernstein-Schurer operators

Title:

King type modification of $q$-Bernstein-Schurer operators

Creator:

Ren, Mei-Ying and Zeng, Xiao-Ming

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:1c5e3f5a-01c3-46cc-8a0d-0285712afea7
uuid:1c5e3f5a-01c3-46cc-8a0d-0285712afea7

Subject:

King type operator, $q$-Bernstein-Schurer operator, Korovich type approximation theorem, rate of convergence, Voronovskaja-type result, and modulus of continuity

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

805-817

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:3

Harvested from:

CDK

Metadata only:

false