Journal ArticleDOI
On q-Parametric Szász-Mirakjan Operators
TLDR
In this paper, the convergence properties of q-parametric Szasz-Mirakjan operators were studied and inequalities for the weighted approximation error were obtained in terms of weighted moduli of continuity.Abstract:
In the present paper, we introduce q-parametric Szasz-Mirakjan operators. We study convergence properties of these operators S
n,q(f). We obtain inequalities for the weighted approximation error of q-Szasz-Mirakjan operators. Such inequalities are valid for functions of polynomial growth and are expressed in terms of weighted moduli of continuity. We also discuss Voronovskaja-type formula for q-Szasz-Mirakjan operators.read more
Citations
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(p,q)-Generalization of Szász–Mirakyan operators
TL;DR: In this paper, the authors introduce new modifications of Szasz-mirakyan operators based on (p,q)-integers, and give a recurrence relation for the moments of new operators.
Journal ArticleDOI
Quantitative q-Voronovskaya and q-Grüss–Voronovskaya-type results for q-Szász operators
TL;DR: In this paper, the authors mainly studied quantitative Voronovskaya-type theorems for q-Szász operators defined in [20] and obtained the quantitative q-VORONOVskaya type theorem in terms of the weighted modulus of continuity of q-derivatives of the approximated function.
The rate of convergence of q-bernstein polynomials for 0 strict inequality q strict inequality 1
TL;DR: For a sequence of q-Bernstein polynomials, the rate of convergence for 0 0, α ≠ 1, and the orders do not depend on α, unlike the classical case.
Journal ArticleDOI
On a Kantorovich Variant of (p,q) -Szász-Mirakjan Operators
TL;DR: In this paper, a Kantorovich variant of -analogue of Szasz-Mirakjan operators is proposed and the moments of the operators are established with the help of a recurrence relation.
Journal ArticleDOI
Approximation Theorems for q-Bernstein-Kantorovich Operators
TL;DR: In this paper, a q-analogue of the Bernstein-Kantorovich operators is introduced and the approximation properties of the q-Bernstein-Kanagalakis operator are investigated.
References
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Journal ArticleDOI
Generalization of S. Bernstein's Polynomials to the Infinite Interval
TL;DR: In this article, the convergence of P(u, x) to f(x) as u −> °o was studied and generalized analogs of known properties of S. Bernstein's approximation polynomials in a finite interval.
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q -Bernstein polynomials and their iterates
TL;DR: It is proved that for a function f analytic in {z: |z| < q + e} the rate of convergence of {Bn(f, q; x)} to f(x) in the norm of C[0,1] has the order q-n (versus 1/n for the classical Bernstein polynomials).
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Some approximation properties of q-Durrmeyer operators
TL;DR: A simple q analogue of well known Durrmeyer operators is introduced and the rate of convergence for q-Durr Meyer operators is established.
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Convergence of Generalized Bernstein Polynomials
TL;DR: It is shown that in general these properties of the sequence {Bn(f, q; x)∞n=1} are essentially different from those in the classical case q=1.