Optimality of generalized Bernstein operators

DOI10.1016/j.jat.2010.03.003zbMath1195.41023arXiv1003.1038OpenAlexW1995772016MaRDI QIDQ979051

Hermann Render, Jésus M. Aldaz

Publication date: 25 June 2010

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

Full work available at URL: https://arxiv.org/abs/1003.1038

zbMATH Keywords

generalized convexityextended Chebyshev spacegeneralized Bernstein operator

Mathematics Subject Classification ID

Approximation by positive operators (41A36)

Related Items (13)

Convergence of rational Bernstein operators ⋮ Bernstein-type operators that reproduce exponential functions ⋮ On the composition and decomposition of positive linear operators (V) ⋮ Weighted approximation by analogues of Bernstein operators for rational functions ⋮ Bivariate Bernstein Chlodovsky Operators Preserving Exponential Functions and Their Convergence Properties ⋮ Bernstein type operators with a better approximation for some functions ⋮ Voronovskaja-type theorem for modified Bernstein operators ⋮ On Szász-Mirakyan operators preserving \(e^{2ax}\), \(a>0\) ⋮ Generalized Bernstein operators on the classical polynomial spaces ⋮ Bernstein operators for extended Chebyshev systems ⋮ Approximation properties of generalized Baskakov-Schurer-Szasz-Stancu operators preserving \(e^{-2ax}\), \(a>0\) ⋮ On sequences of J. P. King-type operators ⋮ Aldaz-Kounchev-Render operators and their approximation properties

Cites Work

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• An extremal property of Bernstein operators
• Bernstein operators for exponential polynomials
• Shape preserving representations for trigonometric polynomial curves
• Critical length for design purposes and extended Chebyshev spaces
• Some results for a class of generalized polynomials
• Bernstein bases in Müntz spaces
• Curve and surface construction using variable degree polynomial splines
• On an extremal relation of Bernstein operators
• On a class of weak Tchebycheff systems
• An extremal property for a class of positive linear operators
• Hadamard-type inequalities for generalized convex functions

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