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On q-Szász-Durrmeyer operators

100%
Mahmudov N., Kaffaoğlu H.
Open Mathematics
|
2010
|
tom 8
|
nr 2
399-409
EN
In the present paper, we introduce the q-Szász-Durrmeyer operators and justify a local approximation result for continuous functions in terms of moduli of continuity. We also discuss a Voronovskaya type result for the q-Szász-Durrmeyer operators.
2
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Approximation properties of q-Baskakov operators

100%
Finta Z., Gupta V.
Open Mathematics
|
2010
|
tom 8
|
nr 1
199-211
EN
We establish direct estimates for the q-Baskakov operator introduced by Aral and Gupta in [2], using the second order Ditzian-Totik modulus of smoothness. Furthermore, we define and study the limit q-Baskakov operator.
3
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On the dependence of parameters in the equivalence theorem for the real method

100%
Cobos F., Fernández-Cabrera L. M., Karadzhov G. E., Kühn T.
Commentationes Mathematicae
|
2015
|
tom 55
|
nr 2
EN
We determine the exact dependence on \(\theta,q,p\) of the constants in the equivalence theorem for the real interpolation method \((A_0,A_1)_{\theta,q}\) with pairs of \(p\)-normed spaces.
4
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Distribution and rearrangement estimates of the maximal function and interpolation

63%
U. Asekritova I., Krugljak N. Y., Maligranda L., Persson L.-E.
Studia Mathematica
|
1997
|
tom 124
|
nr 2
107-132
EN
There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition. Analogous methods allow us to obtain K-functional formulas in terms of the maximal function for couples of weighted $L_p$-spaces.
5
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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
|
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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