The saturation class and iterates of the Bernstein polynomials

DOI10.1016/0021-9045(73)90028-2zbMath0258.41012OpenAlexW2066750469MaRDI QIDQ2559783

Charles A. Micchelli

Publication date: 1973

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

Full work available at URL: https://doi.org/10.1016/0021-9045(73)90028-2

Mathematics Subject Classification ID

Approximation by operators (in particular, by integral operators) (41A35) Saturation in approximation theory (41A40)

Related Items

Convergence of iterated Boolean sums of simultaneous approximants ⋮ Improved rate of approximation by modification of Baskakov operator ⋮ Rate of convergence for certain families of summation-integral type operators ⋮ Approximation theorems for the iterated Boolean sums of Bernstein operators ⋮ On the limits of (linear combinations of) iterates of linear operators ⋮ On the iterates of some Bernstein-type operators ⋮ Some results on modified Szász-Mirakjan operators ⋮ Shape preserving properties of univariate Lototsky-Bernstein operators ⋮ On some approximation processes and their associated parabolic problems ⋮ Limits of certain iterates of Post-Widder operators ⋮ On the numerical solution of Volterra integral equations on equispaced nodes ⋮ \(q\)-Bernstein polynomials and their iterates. ⋮ Asymptotic properties of powers of linear positive operators which preserve \(e_2\) ⋮ Iterated Boolean Sums of Bernstein Type Operators ⋮ Iterates of Markov Operators and Constructive Approximation of Semigroups ⋮ Approximation with one-bit polynomials in Bernstein form ⋮ Strong estimates of the weighted simultaneous approximation by the Bernstein and Kantorovich operators and their iterated Boolean sums ⋮ A new approach to improve the order of approximation of the Bernstein operators: theory and applications ⋮ On \(L_{p}\)-approximation by iterative combination of Bernstein-Durrmeyer polynomials ⋮ The iterative combinations of a new sequence of linear positive operators ⋮ Iterates of Markov operators ⋮ Convergence of Iterated Boolean-type Sums and Their Iterates ⋮ \(K\)-functionals and multivariate Bernstein polynomials ⋮ Unnamed Item ⋮ Convexity and Bernstein polynomials on \(k\)-simploids ⋮ Improved approximation on Durrmeyer-type operators ⋮ Saturation of positive operators ⋮ Unnamed Item ⋮ The eigenstructure of the Bernstein operator ⋮ Unnamed Item ⋮ Some numerical applications of generalized Bernstein operators ⋮ A product integration rule on equispaced nodes for highly oscillating integrals ⋮ On the convergence and iterates of \(q\)-Bernstein polynomials

Cites Work

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• On the adjoint semigroup and some problems in the theory of approximation
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• Iterates of Bernstein polynomials
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• Some remarks on saturation problem in the local approximation. II
• Saturation of positive operators
• Chebyshev Subspaces and Convergence of Positive Linear Operators
• Elementary Solutions for Certain Parabolic Partial Differential Equations
• A General Theorem on the Convergence of Operator Semigroups
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