On Lototsky–Bernstein operators and Lototsky–Bernstein bases

This paper deals with Lupaş post quantum Bernstein operators over arbitrary closed and bounded interval constructed with the help of Lupaş post quantum Bernstein bases. Due to the property that these bases are scale invariant and translation invariant, the derived results on arbitrary intervals are important from computational point of view. Approximation properties of Lupaş post quantum Bernstein operators on arbitrary compact intervals based on Korovkin type theorem are studied. More general situation along all possible cases have been discussed favouring convergence of sequence of Lupaş post quantum Bernstein operators to any continuous function defined on compact interval. Rate of convergence by modulus of continuity and functions of Lipschitz class are computed. Graphical analysis has been presented with the help of MATLAB to demonstrate approximation of continuous functions by Lupaş post quantum Bernstein operators on different compact intervals.

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Lupaş type Bernstein operators on triangles based on quantum analogue

Alexandria Engineering Journal ◽

10.1016/j.aej.2021.04.038 ◽

2021 ◽

Vol 60 (6) ◽

pp. 5909-5919

Author(s):

Asif Khan ◽

M.S. Mansoori ◽

Khalid Khan ◽

M. Mursaleen

Keyword(s):

Bernstein Operators ◽

Quantum Analogue

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

Abstract and Applied Analysis ◽

10.1155/2014/521709 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6 ◽

Cited By ~ 1

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.

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

Expositiones Mathematicae ◽

10.1016/j.exmath.2017.10.001 ◽

2018 ◽

Vol 36 (2) ◽

pp. 143-165

Author(s):

Takis Konstantopoulos ◽

Linglong Yuan ◽

Michael A. Zazanis

Keyword(s):

Limit Theorems ◽

Stochastic Approach ◽

Bernstein Operators

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Approximation of fuzzy numbers by nonlinear Bernstein operators of max-product kind

Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011) ◽

10.2991/eusflat.2011.61 ◽

2011 ◽

Cited By ~ 3

Author(s):

Lucian Coroianu ◽

Sorin G. Gal ◽

Barnabas Bede

Keyword(s):

Fuzzy Numbers ◽

Bernstein Operators

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Novel polynomial Bernstein bases and Bézier curves based on a general notion of polynomial blossoming

Numerical Algorithms ◽

10.1007/s11075-015-0059-6 ◽

2015 ◽

Vol 72 (3) ◽

pp. 605-634 ◽

Cited By ~ 2

Author(s):

Ron Goldman ◽

Plamen Simeonov

Keyword(s):

General Notion ◽

Bezier Curves ◽

Bézier Curves ◽

Bernstein Bases

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CODES AND SHIFTED CODES

International Journal of Algebra and Computation ◽

10.1142/s0218196712500543 ◽

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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