Complete asymptotic expansions related to conjecture on a Voronovskaja-type theorem

DOI10.1016/j.jmaa.2017.09.011zbMath1375.41018OpenAlexW2752978233WikidataQ123269367 ScholiaQ123269367MaRDI QIDQ1674399

Ioan Gavrea, Mircea Ivan

Publication date: 2 November 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.2017.09.011

zbMATH Keywords

asymptotic expansionsBernstein operatorscentral momentsVoronovskaja theoremMeyer-König and Zeller operatorspositive linear operators

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Approximation by positive operators (41A36)

Related Items (8)

King operators which preserve $x^j$ ⋮ Genuine Bernstein-Durrmeyer type operators preserving 1 and \(x^j\) ⋮ Voronovskaja formula for Aldaz-Kounchev-Render operators: uniform convergence ⋮ Aldaz-Kounchev-Render operators on simplices ⋮ Direct and converse theorems for King type operators ⋮ Bernstein type asymptotic evaluations for linear positive operators on \(C\left[ \alpha ,\beta \right\)] ⋮ Voronovskaja type results and their applications ⋮ Aldaz-Kounchev-Render operators and their approximation properties

Cites Work

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• On the rate of convergence of discretely defined operators
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• Shape preserving properties of generalized Bernstein operators on extended Chebyshev spaces
• On Jessen's inequality for convex functions
• The complete asymptotic expansion for the Meyer-König and Zeller operators
• Sharp upper and lower bounds for the moments of Bernstein polynomials
• The Bernstein Voronovskaja-type theorem for positive linear approximation operators
• On the rate of approximation of functions by the Bernstein polynomials
• First order absolute moment of Meyer-König and Zeller operators and their approximation for some absolutely continuous functions
• Bernsteinsche Potenzreihen
• Bernstein Power Series
• MKZ Type Operators Providing a Better Estimation on [1/2, 1)

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