The genuine Bernstein-Durrmeyer operators and quasi-interpolants

DOI10.1007/s00025-012-0247-9zbMath1253.41006OpenAlexW1966346169MaRDI QIDQ1759045

Margareta Heilmann, Martin Wagner

Publication date: 19 November 2012

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-012-0247-9

zbMATH Keywords

Bernstein-type inequalityquasi-interpolationeigenstructuredirect theoremK-functionalgenuine Bernstein-Durrmeyer operatorJackson-Favard-type estimate

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)

Cites Work

• A global inverse theorem for combinations of Bernstein polynomials
• Best polynomial and Durrmeyer approximation in \(L_ p(S)\)
• 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
• The approximation of the continuous functions by means of some linear positive operators
• On genuine Bernstein-Durrmeyer operators
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