scholarly journals Strong inequalities for the iterated Boolean sums of Bernstein operators

2019 ◽  
Vol 64 (3) ◽  
pp. 299-304
Author(s):  
Li Cheng ◽  
◽  
Xinlong Zhou ◽  
◽  
Keyword(s):  
Bernstein Operators ◽  
Boolean Sums

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 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 .

scholarly journals Lupaş type Bernstein operators on triangles based on quantum analogue

2021 ◽  
Vol 60 (6) ◽  
pp. 5909-5919
Author(s):  
Asif Khan ◽  
M.S. Mansoori ◽  
Khalid Khan ◽  
M. Mursaleen
Keyword(s):  
Bernstein Operators ◽  
Quantum Analogue

scholarly journals Approximation by Boolean sums of linear operators: Telyakovskiǐ-type estimates

1990 ◽  
Vol 42 (2) ◽  
pp. 253-266 ◽  
Author(s):  
Jia-Ding Cao ◽  
Heinz H. Gonska
Keyword(s):  
Upper Bound ◽  
Algebraic Polynomial ◽  
Present Note ◽  
Type Inequality ◽  
Linear Operators ◽  
Polynomial Operators ◽  
Boolean Sums ◽  
General Conditions

In the present note we study the question: “Under which general conditions do certain Boolean sums of linear operators satisfy Telyakovskiǐ-type estimates?” It is shown, in particular, that any sequence of linear algebraic polynomial operators satisfying a Timan-type inequality can be modified appropriately so as to obtain the corresponding upper bound of the Telyakovskiǐ-type. Several examples are included.

scholarly journals The Rate of Convergence of Lupasq-Analogue of the Bernstein Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Heping Wang ◽  
Yanbo Zhang
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Bernstein Operators ◽  
Lipschitz Continuous Functions ◽  
Lipschitz Continuous

We discuss the rate of convergence of the Lupasq-analogues of the Bernstein operatorsRn,q(f;x)which were given by Lupas in 1987. We obtain the estimates for the rate of convergence ofRn,q(f)by the modulus of continuity off, and show that the estimates are sharp in the sense of order for Lipschitz continuous functions.

A fully stochastic approach to limit theorems for iterates of Bernstein operators

2018 ◽  
Vol 36 (2) ◽  
pp. 143-165
Author(s):  
Takis Konstantopoulos ◽  
Linglong Yuan ◽  
Michael A. Zazanis
Keyword(s):  
Limit Theorems ◽  
Stochastic Approach ◽  
Bernstein Operators

scholarly journals CODES AND SHIFTED CODES

2012 ◽  
Vol 22 (06) ◽  
pp. 1250054
Author(s):  
J. T. HIRD ◽  
NAIHUAN JING ◽  
ERNEST STITZINGER
Keyword(s):  
Algebraic Structure ◽  
Schur Functions ◽  
Natural Setting ◽  
Bernstein Operators ◽  
Combinatorial Model

The action of the Bernstein operators on Schur functions was given in terms of codes by Carrell and Goulden (2011) and extended to the analog in Schur Q-functions in our previous work. We define a new combinatorial model of extended codes and show that both of these results follow from a natural combinatorial relation induced on codes. The new algebraic structure provides a natural setting for Schur functions indexed by compositions.

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