Complete asymptotic expansion for multivariate Bernstein-Durrmeyer operators and quasi-interpolants

DOI10.1016/j.jat.2009.04.004zbMath1189.41012OpenAlexW2085241588WikidataQ115600868 ScholiaQ115600868MaRDI QIDQ2654455

Ulrich Abel, Elena E. Berdysheva

Publication date: 19 January 2010

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2009.04.004

zbMATH Keywords

positive operatorquasi-interpolantscomplete asymptotic expansionBernstein-Durrmeyer operator

Mathematics Subject Classification ID

Interpolation in approximation theory (41A05) Simultaneous approximation (41A28)

Related Items (4)

Asymptotic properties of Bernstein-Durrmeyer operators ⋮ The Durrmeyer variant of an operator defined by D.D. Stancu ⋮ Asymptotic expansions for Bernstein-Durrmeyer-Chlodovsky polynomials ⋮ Asymptotic behaviour of Jain operators

Cites Work

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• Asymptotic properties of positive summation-integral operators
• Sur l'approximation de fonctions intégrables sur l'interval-0,1-ferme par des polynômes de Bernstein modifies
• Bernstein-Durrmeyer polynomials on a simplex
• Strong converse inequality for the Bernstein-Durrmeyer operator
• The genuine Bernstein-Durrmmeyer operator on a simplex
• New polynomial preserving operators on simplices: direct results
• A generalised beta integral and the limit of the Bernstein--Durrmeyer operator with Jacobi weights
• An identity for multivariate Bernstein polynomials
• The complete asymptotic expansion for Bernstein-Durrmeyer operators with Jacobi weights
• Durrmeyer Operators and Their Natural Quasi-Interpolants
• Approximation processes for fourier-jacobi expansions^†

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