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The Eigenstructure of the Bernstein Operator [PDF]

Journal of Approximation Theory, 2000
The Bernstein operator Bn reproduces the linear polynomials, which are therefore eigenfunctions corresponding to the eigenvalue 1. We determine the rest of the eigenstructure of Bn.
Shaun Cooper, Shayne Waldron
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Comparison of Two-Parameter Bernstein Operator and Bernstein–Durrmeyer Variants

Bulletin of the Iranian Mathematical Society, 2018
Erbay, Hasan/0000-0002-7555-541XThe quantum calculus and the post-quantum calculus have recently gained broad popularity in computational science and engineering due to their applications to diverse areas such as solution of differential equations ...
Ali Aral, Hasan Erbay
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On the Bernstein Operator of S. Morigi and M. Neamtu [PDF]

Results in Mathematics, 2009
We discuss a Bernstein type operator introduced by S. Morigi and M.
Hermann Render
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Convergence in Variation for Bernstein-Type Operators

Mediterranean Journal of Mathematics, 2015
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Bascanbaz-Tunca, Gulen, İNCE İLARSLAN, HATİCE GÜL   +1 more
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A Bernstein type inequality for the Askey–Wilson operator

Journal of Approximation Theory, 2019
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Xin Li 0022, Rajitha Madhushan Ranasinghe   +1 more
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Bernstein-type operators in Chebyshev spaces

Numerical Algorithms, 2009
Let \(I\) denote a real interval with a non-empty interior. An \((n+1)\)-dimensional space \(E_n\subset C^n(I)\) is said to be an extended Chebyshev space on \(I\) if any non-zero element of \(E_n\) vanishes at most \(n\) times in \(I\), counting multiplicities as far as possible for \(C^n\) functions, that is, up to \((n+1)\).
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On approximation by a class of new Bernstein type operators

Applied Mathematics and Computation, 2008
The authors introduce some discrete, respectively integral, operators representing modifications of the classical Bernstein operators. They establish Voronovskaya type formulae and obtain estimates of the error in simultaneous approximation by linear combinations of the new operators.
Naokant Deo, Muhammad Aslam Noor, Mohammad Arif Siddiqui   +2 more
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Applications of the Shorgin Identity to Bernstein Type Operators

Results in Mathematics, 2018
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Ron Goldman, Xiao-Wei Xu, Xiao-Ming Zeng
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Bernstein-Type Operators Diminish the $\phi$-Variation

Constructive Approximation, 1996
We show that a large class of Bernstein-type operators usually considered in approximation theory diminish the total and the fine φ-variation, thus extending a classical result on 1-variation diminution concerning the Bernstein polynomials. Also, the closely related problem of approximation in φ-variation is thoroughly discussed. For these purposes, we
J. A. Adell, J. de la Cal
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A note on Bernstein type operators

Approximation Theory and its Applications, 1992
For Bernstein operators \(B_ n\) one has the direct theorem \[ \| B_ n f-f\|_ \infty\leq C\left\{ w^ 2_ \varphi\left(f,{1\over\sqrt n}\right)_ \infty +{1\over n} \| f\|_ \infty\right\},\quad n\in\mathbb{N}, \] where \(C\) is independent of \(n\) and \(w^ 2_ \varphi(f,\cdot)_ \infty\) denotes the second order Ditzian-Totik modulus of smoothness with ...
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