Results 21 to 30 of about 1,722 (295)

The Eigenstructure of the Bernstein Operator

Journal of Approximation Theory, 2000
The authors determine the eigenvalues and eigenfunctions of the Bernstein operator \(B_n\), the latter are, of course, \(n+1\) polynomials of degrees \(k=0,\dots,n\). They show that the \(k\)th eigen-polynomial \(p^{(n)}_k\) has \(k\) simple zeros in \([0,1]\) and describe \(\lim_{n\to\infty}p^{(n)}_k\), for fixed \(k\).
Cooper, Shaun, Waldron, Shayne
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Bernstein Operators for Exponential Polynomials [PDF]

Constructive Approximation, 2008
Let $L$ be a linear differential operator with constant coefficients of order $n$ and complex eigenvalues $λ_{0},...,λ_{n}$. Assume that the set $U_{n}$ of all solutions of the equation $Lf=0$ is closed under complex conjugation. If the length of the interval $[ a,b] $ is smaller than $π/M_{n}$, where $M_{n}:=\max \left\{| \text{Im}% λ_{j}| :j=0,...,n ...
Aldaz, J. M., Kounchev, Ognyan, Render, Hermann   +2 more
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On the Approximation Properties of q−Analogue Bivariate λ-Bernstein Type Operators

Journal of Function Spaces, 2020
In this article, we establish an extension of the bivariate generalization of the q-Bernstein type operators involving parameter λ and extension of GBS (Generalized Boolean Sum) operators of bivariate q-Bernstein type.
Edmond Aliaga, Behar Baxhaku
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Rate of Weighted Statistical Convergence for Generalized Blending-Type Bernstein-Kantorovich Operators

Mathematics, 2022
An alternative approach, known today as the Bernstein polynomials, to the Weierstrass uniform approximation theorem was provided by Bernstein. These basis polynomials have attained increasing momentum, especially in operator theory, integral equations ...
Faruk Özger, Ekrem Aljimi, Merve Temizer Ersoy   +2 more
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Approximation Order for Multivariate Durrmeyer Operators with Jacobi Weights

Abstract and Applied Analysis, 2011
Using the equivalence relation between K-functional and modulus of smoothness, we establish a strong direct theorem and an inverse theorem of weak type for multivariate Bernstein-Durrmeyer operators with Jacobi weights on a simplex in this paper. We also
Jianjun Wang, Chan-Yun Yang, Shukai Duan
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On bivariate Bernstein-Chlodowsky operators [PDF]

Journal of Classical Analysis, 2016
Summary: This work relates to the bivariate Bernstein-Chlodowsky operator which is not a tensor product construction. We show that the operator preserves some properties of the original function, for example, function of modulus of continuity, Lipschitz constant, and a kind of monotony.
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The Diagonalisation of the Multivariate Bernstein Operator

Journal of Approximation Theory, 2002
The paper is split into five sections. In Section 1 is defined the multivariate Bernstein operator \(B_n\) of degree \(n\) for a simplex in \(\mathbb{R}^s\), establishing notations and some technical results. In Section 2, the authors show that \(B_n\) is diagonalisable with the same eigenvalues as the univariate Bernstein operator, i.e.
Shaun Cooper, Shayne Waldron
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A Generalization of Bernstein–Kantorovič Operators

Journal of Mathematical Analysis and Applications, 2000
The authors introduce a double sequence \((L_n^{\langle k \rangle}: n\geq 1,k\geq 0)\) of linear polynomial operators which includes, as particular cases, the Bernstein, Kantorovič and Cao operators. For the operators \(L_n^{\langle k\rangle}\) the authors discuss several approximation properties: the convergence properties, the preservation of global ...
de la Cal, Jesús, Valle, Ana M
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Genuine modified Bernstein–Durrmeyer operators [PDF]

Journal of Inequalities and Applications, 2018
The present paper deals with genuine Bernstein-Durrmeyer operators which preserve some certain functions. The rate of convergence of new operators via a Peetre [Formula: see text]-functional and corresponding modulus of smoothness, quantitative Voronovskaya type theorem and Grüss-Voronovskaya type theorem in quantitative mean are discussed.
Syed Abdul Mohiuddine, Tuncer Acar, Mohammed A. Alghamdi   +2 more
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Bivariate Bernstein type operators

Applied Mathematics and Computation, 2016
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Gülen Bascanbaz Tunca, Hatice Gül Ince-Ilarslan, Aysegül Erençin   +2 more
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