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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Rates of convergence of Chlodovsky-Kantorovich polynomials in classes of locally integrable functions

100%
Pych-Taberska P.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2009
|
tom 29
|
nr 1
53-66
EN
In this paper we establish an estimation for the rate of pointwise convergence of the Chlodovsky-Kantorovich polynomials for functions f locally integrable on the interval [0,∞). In particular, corresponding estimation for functions f measurable and locally bounded on [0,∞) is presented, too.
2
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Pointwise approximation by Meyer-König and Zeller operators

100%
Zeng X.-M., Zhao J.-N.
Annales Polonici Mathematici
|
2000
|
tom 73
|
nr 2
185-196
EN
We study the rate of pointwise convergence of Meyer-König and Zeller operators for bounded functions, and get an asymptotically optimal estimate.
3
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On some class of exponential type operators

100%
Tyliba A., Wachnicki E.
Commentationes Mathematicae
|
2005
|
tom 45
|
nr 1
EN
Starting from a differential equation \(\frac{\partial}{\partial t} W (\lambda, t, u)=\frac{\lambda(u-t)}{p(t)}W(\lambda,t,u)-\beta W(\lambda,t,u)\) for the kernel of an operator \(S_\lambda(f,t) = \int_{A}^{B}W(\lambda,t,u)f(u)du\) with the normalization condition \(\int_A^B W(\lambda, t, u)du = 1\) we prove some properties which are similar to properties proved by Ismail and May for the exponential operators. In particular, we show that all these operators are approximation operators. Moreover, a method of determining \(S_\lambda\) for a given function \(p\) is introduced.
4
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On the rates of convergence of Chlodovsky-Kantorovich operators and their Bézier variant

88%
Pych-Taberska P., Karsli H.
Commentationes Mathematicae
|
2009
|
tom 49
|
nr 2
EN
In the present paper we consider the Bézier variant of Chlodovsky-Kantorovich operators \(K_{n−1,\alpha} f\) for functions \(f\) measurable and locally bounded on the interval \([0,\infty)\). By using the Chanturiya modulus of variation we estimate the rate of pointwise convergence of \(K_{n−1,\alpha} f (x)\) at those \(x \gt 0\) at which the one-sided limits \(f (x+)\), \(f(x-)\) exist.
5
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Approximation by bivariate Mazhar-Totik operators

75%
Wachnicki E.
Commentationes Mathematicae
|
2010
|
tom 50
|
nr 2
EN
The aim of this paper is to study a bivariate version of the operator investigated in [2], [4]. We shall present Voronovskaya type theorem and theorems giving a rate of convergence of this operator. Some applications for the limit problem are indicated.
6
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Representation formulae for (C₀) m-parameter operator semigroups

63%
Zhou M., Anastassiou G.
Annales Polonici Mathematici
|
1996
|
tom 63
|
nr 3
247-272
EN
Some general representation formulae for (C₀) m-parameter operator semigroups with rates of convergence are obtained by the probabilistic approach and multiplier enlargement method. These cover all known representation formulae for (C₀) one- and m-parameter operator semigroups as special cases. When we consider special semigroups we recover well-known convergence theorems for multivariate approximation operators.
7
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Refined rates of bias convergence for generalized L-Statistics in the i.i.d. case

63%
Anastassiou G. A., Rychlik T.
Applicationes Mathematicae
|
1999
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tom 26
|
nr 4
437-455
EN
Using tools of approximation theory, we evaluate rates of bias convergence for sequences of generalized L-statistics based on i.i.d. samples under mild smoothness conditions on the weight function and simple moment conditions on the score function. Apart from standard methods of weighting, we introduce and analyze L-statistics with possibly random coefficients defined by means of positive linear functionals acting on the weight function.
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