A note on (p,q) $(p,q)$-Bernstein polynomials and their applications based on (p,q) $(p,q)$-calculus [PDF]
Journal of Inequalities and Applications, 2018 Nowadays (p,q) $(p,q)$-Bernstein polynomials have been studied in many different fields such as operator theory, CAGD, and number theory. In order to obtain the fundamental properties and results of Bernstein polynomials by using (p,q) $(p,q)$-calculus ...
Erkan Agyuz, Mehmet Acikgoz
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Degenerate Bernstein polynomials [PDF]
Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2018 9
Taekyun Kim, Dae San Kim, Dae San Kim
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Representation of ( p , q ) $(p,q)$ -Bernstein polynomials in terms of ( p , q ) $(p,q)$ -Jacobi polynomials [PDF]
Journal of Inequalities and Applications, 2017 A representation of ( p , q ) $(p,q)$ -Bernstein polynomials in terms of ( p , q ) $(p,q)$ -Jacobi polynomials is obtained.
F Soleyman +3 more
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Convergence of Generalized Bernstein Polynomials
Journal of Approximation Theory, 2002 Let \(f\in C[0,1]\), \(q\in (0,1)\) and \(B_n(f,q;x)\) be generalized Bernstein polynomials based on \(q\)-integers. These polynomials were introduced by G. M. Phillips in 1997. The authors study convergence properties of the sequence \(\{B_n(f,q;x)\}^\infty_{n=1}\).
Sofiya Ostrovska
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Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials [PDF]
The Scientific World Journal, 2014 In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system.
Hasib Khan +4 more
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Some identities of degenerate Euler polynomials associated with degenerate Bernstein polynomials
Journal of Inequalities and Applications, 2019 In this paper, we investigate some properties and identities for degenerate Euler polynomials in connection with degenerate Bernstein polynomials by means of fermionic p-adic integrals on Zp $\mathbb{Z}_{p}$ and generating functions.
Taekyun Kim, Dae San Kim, Han Young Kim
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Some Identities on Degenerate Bernstein and Degenerate Euler Polynomials
Mathematics, 2019 In recent years, intensive studies on degenerate versions of various special numbers and polynomials have been done by means of generating functions, combinatorial methods, umbral calculus, p-adic analysis and differential equations.
Taekyun Kim, Dae San Kim
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On Better Approximation of the Squared Bernstein Polynomials [PDF]
مجلة جامعة الانبار للعلوم الصرفة, 2022 The present paper is defined a new better approximation of the squared Bernstein polynomials. This better approximation has been built on a positive function defined on the interval [0,1] which has some properties.
Rafah Katham, Ali Mohammad
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Rough statistical convergence on triple sequence of the Bernstein operator of random variables in probability [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2019 This paper aims to improve further on the work of Phu (2001), Aytar (2008), and Ghosal (2013). We propose a new apporach to extend the application area of rough statistical convergence usually used in triple sequence of the Bernstein operator of real ...
Nagarajan Subramanian +2 more
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On Bernstein’s inequality for polynomials [PDF]
Analysis and Mathematical Physics, 2019 Bernstein's classical inequality asserts that given a trigonometric polynomial $T$ of degree $n\geq1$, the sup-norm of the derivative of $T$ does not exceed $n$ times the sup-norm of $T$. We present various approaches to prove this inequality and some of its natural extensions/variants, especially when it comes to replacing the sup-norm with the $L^p ...
Queffélec, Hervé, Zarouf, Rachid
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