Direct and inverse theorems for Bernstein polynomials in the space of Riemann integrable functions

DOI10.1007/BF01889606zbMath0689.41014OpenAlexW1986247933MaRDI QIDQ581792

Erich van Wickeren

Publication date: 1989

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01889606

zbMATH Keywords

Bernstein operatorRiemann integrable functionssecond weighted Ditzian-Ivanov-Totik modulus of continuity

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximation by positive operators (41A36) Inverse theorems in approximation theory (41A27)

Related Items (3)

Sequential convergence and approximation in the space of Riemann integrable functions ⋮ A sharp error bound in terms of an averaged modulus of smoothness for Fourier Lagrange coefficients ⋮ Direct and converse results for multivariate generalized Bernstein polynomials

Cites Work

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• On the Riemann convergence of positive linear operators
• Converse theorems for approximation by Bernstein polynomials in \(L_ p[0,1\) \((1<p<\infty)\)]
• Steckin-Marchaud-type inequalities in connection with Bernstein polynomials
• Sequential convergence and approximation in the space of Riemann integrable functions
• On interpolation of L//p[a,b and weighted Sobolev spaces]
• An interpolation theorem and its applications to positive operators

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