\(K\)-functionals and multivariate Bernstein polynomials

DOI10.1016/j.jat.2008.03.011zbMath1204.41010OpenAlexW2082591995MaRDI QIDQ999281

Chunmei Ding, Feilong Cao

Publication date: 3 February 2009

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

Full work available at URL: https://doi.org/10.1016/j.jat.2008.03.011

zbMATH Keywords

\(K\)-functionalmultivariate Bernstein polynomialsapproximation orderinverse theoremsdirect theoremsBoolean sums

Mathematics Subject Classification ID

Approximation by other special function classes (41A30) Inverse theorems in approximation theory (41A27)

Related Items (7)

Inequalities for a class of multivariate operators ⋮ Unnamed Item ⋮ On simultaneous approximation by iterated Boolean sums of Bernstein operators ⋮ Bivariate Bernstein type operators ⋮ Strong estimates of the weighted simultaneous approximation by the Bernstein and Kantorovich operators and their iterated Boolean sums ⋮ Random sampling scattered data with multivariate Bernstein polynomials ⋮ Strong converse inequality for linear combinations of Szász-Mirakjan operators

Cites Work

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• Inverse theorems for multidimensional Bernstein operators
• An interpolation theorem and its applications to positive operators
• \(K\)-moduli, moduli of smoothness, and Bernstein polynomials on a simplex
• Multivariate Bernstein and Markov inequalities
• Optimal approximation class for multivariate Bernstein operators
• Approximation by multivariate Bernstein operators
• Weighted approximation by multidimensional Bernstein operators
• Convergence of iterated Boolean sums of simultaneous approximants
• The lower estimate for linear positive operators. II
• Approximation theorems for the iterated Boolean sums of Bernstein operators
• On the limits of (linear combinations of) iterates of linear operators
• Derivatives of multidimensional Bernstein operators and smoothness
• Lagrange and least-squares polynomials as limits of linear combinations of iterates of Bernstein and Durrmeyer polynomials
• Polynomial approximation in \(L_ p(S)\) for \(p>0\)
• The saturation class and iterates of the Bernstein polynomials
• ON THE ITERATIVE COMBINATIONS OF BERNSTEIN POLYNOMIALS
• Approximation by Bernstein Polynomials
• Strong converse inequalities

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