On Simultaneous Approximation by Iterated Boolean Sums of Bernstein Operators

2014 ◽  
Vol 66 (1-2) ◽  
pp. 21-41 ◽  
Author(s):  
Borislav R. Draganov
Keyword(s):  
Simultaneous Approximation ◽  
Bernstein Operators ◽  
Boolean Sums

The Bernstein operators on any finite interval revisited

2020 ◽  
Vol 29 (1) ◽  
pp. 01-08
Author(s):  
DAN BARBOSU
Keyword(s):  
Simultaneous Approximation ◽  
Finite Interval ◽  
Bernstein Polynomials ◽  
Bernstein Operators ◽  
Approximation Properties

One studies simultaneous approximation properties of fundamental Bernstein polynomials involved in the construction of the mentioned operators.

scholarly journals Lagrange-type operators associated with Uan

2014 ◽  
Vol 96 (110) ◽  
pp. 159-168 ◽  
Author(s):  
Heiner Gonska ◽  
Ioan Raşa ◽  
Elena-Dorina Stănilă
Keyword(s):  
Main Tool ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Bernstein Operators ◽  
Boolean Sums ◽  
Derivatives Of

We consider a class of positive linear operators which, among others, constitute a link between the classical Bernstein operators and the genuine Bernstein-Durrmeyer mappings. The focus is on their relation to certain Lagrange-type interpolators associated to them, a well known feature in the theory of Bernstein operators. Considerations concerning iterated Boolean sums and the derivatives of the operator images are included. Our main tool is the eigenstructure of the members of the class.

scholarly journals Approximation of Finite Hilbert and Hadamard Transforms by Using Equally Spaced Nodes

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 542
Author(s):  
Frank Filbir ◽  
Donatella Occorsio ◽  
Woula Themistoclakis
Keyword(s):  
Simultaneous Approximation ◽  
Bernstein Polynomials ◽  
Reference Interval ◽  
Pointwise Estimates ◽  
Numerical Tests ◽  
Equidistant Points ◽  
Hadamard Transforms ◽  
Boolean Sums ◽  
Generalized Bernstein Polynomials ◽  
Theoretical Results

In the present paper, we propose a numerical method for the simultaneous approximation of the finite Hilbert and Hadamard transforms of a given function f, supposing to know only the samples of f at equidistant points. As reference interval we consider [ − 1 , 1 ] and as approximation tool we use iterated Boolean sums of Bernstein polynomials, also known as generalized Bernstein polynomials. Pointwise estimates of the errors are proved, and some numerical tests are given to show the performance of the procedures and the theoretical results.

Simultaneous approximation by Bernstein operators in Hölder norms

2012 ◽  
Vol 286 (4) ◽  
pp. 349-359 ◽  
Author(s):  
Heiner Gonska ◽  
Jürgen Prestin ◽  
Gancho Tachev ◽  
Ding-xuan Zhou
Keyword(s):  
Simultaneous Approximation ◽  
Bernstein Operators

scholarly journals Phillips-Type q -Bernstein Operators on Triangles

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Asif Khan ◽  
M. S. Mansoori ◽  
Khalid Khan ◽  
M. Mursaleen
Keyword(s):  
Modulus Of Continuity ◽  
Classical Case ◽  
Approximation Formula ◽  
Graphical Representations ◽  
Bernstein Operators ◽  
Quantum Analogue ◽  
Boolean Sums ◽  
Peano’S Theorem

The purpose of the paper is to introduce a new analogue of Phillips-type Bernstein operators B m , q u f u , v and B n , q v f u , v , their products P m n , q f u , v and Q n m , q f u , v , their Boolean sums S m n , q f u , v and T n m , q f u , v on triangle T h , which interpolate a given function on the edges, respectively, at the vertices of triangle using quantum analogue. Based on Peano’s theorem and using modulus of continuity, the remainders of the approximation formula of corresponding operators are evaluated. Graphical representations are added to demonstrate consistency to theoretical findings. It has been shown that parameter q provides flexibility for approximation and reduces to its classical case for q = 1 .

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