An answer to a conjecture on Bernstein operators

DOI10.1016/j.jmaa.2012.01.021zbMath1254.41017OpenAlexW1978214404WikidataQ123121001 ScholiaQ123121001MaRDI QIDQ408254

Mircea Ivan, Ioan Gavrea

Publication date: 29 March 2012

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.2012.01.021

zbMATH Keywords

asymptotic expansionsBernstein operatorsVoronovskaja type theorems

Mathematics Subject Classification ID

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

Related Items (19)

Improved rate of approximation by modification of Baskakov operator ⋮ Expansion of moments of Bernstein polynomials ⋮ Convergence of rational Bernstein operators ⋮ Sharp upper and lower bounds for the moments of Bernstein polynomials ⋮ Complete asymptotic expansions related to conjecture on a Voronovskaja-type theorem ⋮ Modified Kantorovich operators with better approximation properties ⋮ On the Asymptotic Behavior of Sequences of Positive Linear Approximation Operators ⋮ Estimates for the moments of Bernstein polynomials ⋮ On the rate of convergence of discretely defined operators ⋮ A new approach to improve the order of approximation of the Bernstein operators: theory and applications ⋮ Quantitative generalized Voronovskaja's formulae for Bernstein polynomials ⋮ The Bernstein Voronovskaja-type theorem for positive linear approximation operators ⋮ Approximation with certain exponential operators ⋮ On convergence of derivatives of Voronovskaja-type expansion for Bernstein type operators ⋮ Approximation by modified Kantorovich-Stancu operators ⋮ Better numerical approximation by Durrmeyer type operators ⋮ Semi-discrete quantitative Voronovskaya-type theorems for positive linear operators ⋮ Modified \(\alpha\)-Bernstein operators with better approximation properties ⋮ Modifiedρ-Bernstein Operators for Functions of Two Variables

Cites Work

• The complete asymptotic expansion for Bernstein operators
• On the rate of approximation of functions by the Bernstein polynomials
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