Convergence of iterates of genuine and ultraspherical Durrmeyer operators to the limiting semigroup: \(C^{2}\)-estimates

DOI10.1016/j.jat.2008.11.002zbMath1184.41005OpenAlexW2072880980MaRDI QIDQ1041633

Ioan Raşa, Margareta Heilmann, Heinz H. Gonska

Publication date: 3 December 2009

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

Full work available at URL: https://doi.org/10.1016/j.jat.2008.11.002

zbMATH Keywords

semigroupmoduli of smoothnessdegree of approximationgenuine Bernstein-Durrmeyer operatorsBernstein-Durrmeyer operators with ultraspherical weightsoperators on Banach spaces

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25) Approximation by positive operators (41A36)

Related Items (4)

On the convergence properties of sampling Durrmeyer‐type operators in Orlicz spaces ⋮ Gamma-type operators and the Black-Scholes semigroup ⋮ Quantitative results for the limiting semigroup generated by the multidimensional Bernstein operators ⋮ Geometric series of positive linear operators and the inverse Voronovskaya theorem on a compact interval

Cites Work

• The limiting semigroup of the Bernstein iterates: degree of convergence
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