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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.
2
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Approximation by the Bézier variant of the MKZ-Kantorovich operators in the case α < 1

100%
Zeng X.-M., Gupta V.
Open Mathematics
|
2009
|
tom 7
|
nr 3
550-557
EN
The pointwise approximation properties of the Bézier variant of the MKZ-Kantorovich operators $$ \hat M_{n,\alpha } (f,x) $$ for α ≥ 1 have been studied in [Comput. Math. Appl., 39 (2000), 1-13]. The aim of this paper is to deal with the pointwise approximation of the operators $$ \hat M_{n,\alpha } (f,x) $$ for the other case 0 < α < 1. By means of some new techniques and new inequalities we establish an estimate formula on the rate of convergence of the operators $$ \hat M_{n,\alpha } (f,x) $$ for the case 0 < α < 1. In the end we propose the q-analogue of MKZK operators.
3
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Statistical approximation of Baskakov and Baskakov-Kantorovich operators based on the q-integers

100%
Mahmudov N.
Open Mathematics
|
2010
|
tom 8
|
nr 4
816-826
EN
In the present paper we introduce and investigate weighted statistical approximation properties of a q-analogue of the Baskakov and Baskakov-Kantorovich operators. By using a weighted modulus of smoothness, we give some direct estimations for error in the case 0 < q < 1.
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