L p approximation by general Bernstein-Durrmeyer operator defined on simplex

DOI10.1007/BF02835257zbMath1074.41018MaRDI QIDQ4670344

Feilong Cao

Publication date: 18 April 2005

Published in: Analysis in Theory and Applications (Search for Journal in Brave)

zbMATH Keywords

moduli of smoothnessdegree of approximationBernstein-Durrmeyer operatorsdirect theoreminverse theoremmultidimensional \(L^p\) approximation

Mathematics Subject Classification ID

Multidimensional problems (41A63) Rate of convergence, degree of approximation (41A25) Approximation by positive operators (41A36) Inverse theorems in approximation theory (41A27)

Cites Work

• Bernstein-type operators and their derivatives
• On multivariate approximation by Bernstein-type polynomials
• Inverse theorems for multidimensional Bernstein operators
• Steckin-Marchaud-type inequalities in connection with Bernstein polynomials
• \(L_ p\)-saturation of some modified Bernstein operators
• A global inverse theorem on simultaneous approximation by Bernstein- Durrmeyer operators
• Bernstein-Durrmeyer polynomials on a simplex
• Inverse theorems for multidimensional Bernstein-Durrmeyer operators in \(L_ p\)
• \(K\)-moduli, moduli of smoothness, and Bernstein polynomials on a simplex
• Best polynomial and Durrmeyer approximation in \(L_ p(S)\)
• Strong converse inequality for the Bernstein-Durrmeyer operator
• Optimal approximation class for multivariate Bernstein operators
• Multivariate Stancu operators defined on a simplex.
• The lower estimate for linear positive operators. I
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