Shape preserving properties of generalized Bernstein operators on extended Chebyshev spaces
From MaRDI portal
Publication:849053
DOI10.1007/s00211-009-0248-0zbMath1184.41011arXiv0805.1614OpenAlexW3104025487MaRDI QIDQ849053
Hermann Render, Jésus M. Aldaz, Ognyan Kounchev
Publication date: 24 February 2010
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0805.1614
Best approximation, Chebyshev systems (41A50) Approximation by operators (in particular, by integral operators) (41A35)
Related Items (42)
Greville abscissae of totally positive bases ⋮ Approximation on a new class of Szász-Mirakjan operators and their extensions in Kantorovich and Durrmeyer variants with applicable properties ⋮ Approximation by Chebyshevian Bernstein operators versus convergence of dimension elevation ⋮ Design with quasi extended Chebyshev piecewise spaces ⋮ Convergence of rational Bernstein operators ⋮ New estimates for the differences of positive linear operators ⋮ Shape preserving properties of univariate Lototsky-Bernstein operators ⋮ Complete asymptotic expansions related to conjecture on a Voronovskaja-type theorem ⋮ A proof of a conjecture about the asymptotic formula of a Bernstein type operator ⋮ King operators which preserve $x^j$ ⋮ New quantitative results for the convergence of the iterates of some positive linear operators ⋮ Asymptotic formulae via a Korovkin-type result ⋮ Genuine Bernstein-Durrmeyer type operators preserving 1 and \(x^j\) ⋮ Voronovskaja formula for Aldaz-Kounchev-Render operators: uniform convergence ⋮ Aldaz-Kounchev-Render operators on simplices ⋮ New rational cubic trigonometric B-spline curves with two shape parameters ⋮ Critical lengths of cycloidal spaces are zeros of Bessel functions ⋮ Direct and converse theorems for King type operators ⋮ A note on the fixed points of positive linear operators ⋮ A class of Markov type operators which preserve \(e_j\), \(j \geqslant 1\) ⋮ Finding all systems of weight functions associated with a given extended Chebyshev space ⋮ New multivariate and univariate Aldaz-Kounchev-Render type operators ⋮ Bernstein type operators having 1 and \(x^j\) as fixed points ⋮ Bernstein-type operators which preserve polynomials ⋮ The iterates of positive linear operators preserving constants ⋮ On Lototsky-Bernstein operators and Lototsky-Bernstein bases ⋮ Voronovskaya type results for special sequences of operators ⋮ Quadratic convergence of approximations by CCC-Schoenberg operators ⋮ Voronovskaja-type theorem for modified Bernstein operators ⋮ Generalized Bernstein operators on the classical polynomial spaces ⋮ Asymptotic behaviour of the iterates of positive linear operators ⋮ Optimality of generalized Bernstein operators ⋮ Bernstein operators for extended Chebyshev systems ⋮ Chebyshev--Schoenberg operators ⋮ Differences of positive linear operators on simplices ⋮ Nested sequences of rational spaces: Bernstein approximation, dimension elevation, and Pólya-type theorems on positive polynomials ⋮ A Quantitative Variant of Voronovskaja's Theorem for King-Type Operators ⋮ VORONOVSKAYA TYPE RESULTS AND OPERATORS FIXING TWO FUNCTIONS ⋮ New properties of operators preserving exponentials ⋮ A totally positive basis for circle approximations ⋮ Note on a Korovkin-type theorem ⋮ Aldaz-Kounchev-Render operators and their approximation properties
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Bernstein operators for extended Chebyshev systems
- Chebyshev spaces and Bernstein bases
- Shape preservation regions for six-dimensional spaces
- Bernstein operators for exponential polynomials
- Totally positive bases for shape preserving curve design and optimality of \(B\)-splines
- C-curves: An extension of cubic curves
- Positive linear operators which preserve \(x^2\)
- Blossoms and optimal bases
- On the optimal stability of bases of univariate functions
- On hyperbolic splines
- Critical length for design purposes and extended Chebyshev spaces
- Shape preserving representations and optimality of the Bernstein basis
- Null spaces of differential operators, polar forms, and splines
- Some results for a class of generalized polynomials
- Bernstein bases in Müntz spaces
- Curve and surface construction using variable degree polynomial splines
- On a class of weak Tchebycheff systems
- Stieltjes integral representation of convex functions
- Hadamard-type inequalities for generalized convex functions
- On the optimal stability of the Bernstein basis
- On Descartes' rules of signs and their exactness
- On the Hermite interpolation
- Shape preserving alternatives to the rational Bézier model
This page was built for publication: Shape preserving properties of generalized Bernstein operators on extended Chebyshev spaces
