Bernstein-Durrmeyer polynomials on a simplex

DOI10.1016/0021-9045(92)90104-VzbMath0754.41005OpenAlexW2019673087MaRDI QIDQ1185259

Hubert Berens, Yuan Xu, Hans Joachim Schmid

Publication date: 28 June 1992

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

Full work available at URL: https://doi.org/10.1016/0021-9045(92)90104-v

zbMATH Keywords

Bernstein-Durrmeyer polynomialsPeetre \(K\)-modulussatration class

Mathematics Subject Classification ID

Approximation by polynomials (41A10) Saturation in approximation theory (41A40)

Related Items (22)

Riesz transforms and fractional integration for orthogonal expansions on spheres, balls and simplices ⋮ Jacobi polynomials in Bernstein form ⋮ Regularity properties of semigroups generated by some Fleming--Viot type operators ⋮ An identity for multivariate Bernstein polynomials ⋮ Complete asymptotic expansion for multivariate Bernstein-Durrmeyer operators and quasi-interpolants ⋮ Strong converse inequalities for the weighted multivariate Bernstein-Durrmeyer operator on the simplex via multipliers ⋮ On the scientific work of Kunyang Wang ⋮ Relations between anisotropic Besov spaces and multivariate Bernstein-Durrmeyer operators ⋮ Bernstein-type operators on the unit disk ⋮ Applications of the Bernstein-Durrmeyer operators in estimating the norm of Mercer kernel matrices ⋮ Approximation on simplices with respect to weighted Sobolev norms ⋮ \(K\)-moduli, moduli of smoothness, and Bernstein polynomials on a simplex ⋮ Learning rates for regularized classifiers using multivariate polynomial kernels ⋮ Approximation order for multivariate Durrmeyer operators with Jacobi weights ⋮ Multivariate Bernstein operators and redundant systems ⋮ New polynomial preserving operators on simplices: direct results ⋮ Approximation by the Bernstein-Durrmeyer operator on a simplex ⋮ L p approximation by general Bernstein-Durrmeyer operator defined on simplex ⋮ Moduli of smoothness and approximation on the unit sphere and the unit ball ⋮ \(K\)-functional, weighted moduli of smoothness, and best weighted polynomial approximation on a simplex ⋮ Simultaneous \(\mathbf L^p\)-approximation order for neural networks ⋮ Generalized Bernstein-Durrmeyer operators and the associated limit semigroup

Cites Work

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• Bernstein-type operators and their derivatives
• On multivariate approximation by Bernstein-type polynomials
• Sur l'approximation de fonctions intégrables sur l'interval-0,1-ferme par des polynômes de Bernstein modifies
• \(K\)-moduli, moduli of smoothness, and Bernstein polynomials on a simplex

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