Approximation of functions by a new family of generalized Bernstein operators

DOI10.1016/j.jmaa.2016.12.075zbMath1357.41015OpenAlexW2571446777WikidataQ56227923 ScholiaQ56227923MaRDI QIDQ511236

Zhi Liu, Jin Xie, Xiao-yan Chen, Jie-qing Tan

Publication date: 14 February 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.12.075

zbMATH Keywords

Bernstein operatormodulus of continuityshape-preserving approximation\(\alpha\)-Bernstein operatorWeierstrass approximation theorem

Mathematics Subject Classification ID

Approximation by operators (in particular, by integral operators) (41A35) Approximation by positive operators (41A36)

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Cites Work

• On generalized integral Bernstein operators based on \(q\)-integers
• Generalized Voronovskaja theorem for \(q\)-Bernstein polynomials
• Bernstein-type operators which preserve polynomials
• \(q\)-Bernstein-Schurer-Durrmeyer type operators for functions of one and two variables
• Convergence in variation for Bernstein-type operators
• Stancu-Schurer-Kantorovich operators based on \(q\)-integers
• Statistical approximation by Kantorovich-type discrete \(q\)-beta operators
• Rate of approximation by finite iterates of \(q\)-Durrmeyer operators
• Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators
• A short note on approximation properties of stancu generalization of \(q\)-Durrmeyer operators
• On a quasi-interpolating Bernstein operator
• On approximation of continuous and of analytic functions
• The rate of convergence ofq-Durrmeyer operators for 0<q<1
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