Best polynomial and Durrmeyer approximation in \(L_ p(S)\)

DOI10.1016/0019-3577(91)90029-7zbMath0756.41033OpenAlexW1994110332MaRDI QIDQ1192451

Z. Ditzian, Weiyu Chen

Publication date: 27 September 1992

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0019-3577(91)90029-7

zbMATH Keywords

best \(L_ p\)-approximation operatorDurrmeyer-Bernstein polynomialKantorovich-Bernstein operator

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25)

Related Items (6)

Applications of the Bernstein-Durrmeyer operators in estimating the norm of Mercer kernel matrices ⋮ The convergence rate for a \(K\)-functional in learning theory ⋮ The genuine Bernstein-Durrmeyer operators and quasi-interpolants ⋮ The equivalence relations between the best approximation and linear operators approximation in a Besov space ⋮ L p approximation by general Bernstein-Durrmeyer operator defined on simplex ⋮ \(K\)-functional, weighted moduli of smoothness, and best weighted polynomial approximation on a simplex

Cites Work

• Bernstein-type operators and their derivatives
• On multivariate approximation by Bernstein-type polynomials
• A global inverse theorem for combinations of Bernstein polynomials
• An interpolation theorem and its applications to positive operators
• Multivariate Bernstein and Markov inequalities
• Remarks on Besov Spaces and Best Polynomial Approximation
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