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1
Content available remote

Statistical approximation properties of q-Baskakov-Kantorovich operators

100%
Gupta V., Radu C.
Open Mathematics
|
2009
|
tom 7
|
nr 4
809-818
EN
In the present paper we introduce a q-analogue of the Baskakov-Kantorovich operators and investigate their weighted statistical approximation properties. By using a weighted modulus of smoothness, we give some direct estimations for error in case 0 < q < 1.
2
Content available remote

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.
3
Content available remote

On an approximation processes in the space of analytical functions

100%
Gadjiev A., Ghorbanalizadeh A.
Open Mathematics
|
2010
|
tom 8
|
nr 2
389-398
EN
In this paper we obtain various approximation theorems by means of k-positive linear operators defined on the space of all analytic functions on a bounded domain of the complex plane.
4
Content available remote

Statistical approximation to Bögel-type continuous and periodic functions

100%
Dirik F., Duman O., Demirci K.
Open Mathematics
|
2009
|
tom 7
|
nr 3
539-549
EN
In this paper, considering A-statistical convergence instead of Pringsheim’s sense for double sequences, we prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on the space of all real valued Bögel-type continuous and periodic functions on the whole real two-dimensional space. A strong application is also presented. Furthermore, we obtain some rates of A-statistical convergence in our approximation.
5
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Lacunary equi-statistical convergence of positive linear operators

76%
Aktuğlu H., Gezer H.
Open Mathematics
|
2009
|
tom 7
|
nr 3
558-567
EN
In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin type approximation theorem via lacunary equi-statistical convergence is proved. Moreover it is shown that our Korovkin type approximation theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. Finally the rates of lacunary equi-statistical convergence by the help of modulus of continuity of positive linear operators are studied.
6
Content available remote

A new approach to nonlinear singular integral operators depending on three parameters

76%
Uysal G.
Open Mathematics
|
2016
|
tom 14
|
nr 1
897-907
EN
In this paper, we present some theorems on weighted approximation by two dimensional nonlinear singular integral operators in the following form: T λ ( f ; x , y ) = ∬ R 2 ( t − x , s − y , f ( t , s ) ) d s d t , ( x , y ) ∈ R 2 , λ ∈ Λ , $${T_\lambda }(f;x,y) = \iint\limits_{{\mathbb{R}^2}} {(t - x,s - y,f(t,s))dsdt,\;(x,y) \in {\mathbb{R}^2},\lambda \in \Lambda ,}$$ where Λ is a set of non-negative numbers with accumulation point λ0.
7
Content available remote

Approximation properties of q-Baskakov operators

76%
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.
8
Content available remote

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

76%
Zeng X.-M., Gupta V.
Open Mathematics
|
2009
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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.
9
Content available remote

Statistical approximation of Baskakov and Baskakov-Kantorovich operators based on the q-integers

76%
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.
10
Content available remote

A note on the rate of convergence for Chebyshev-Lobatto and Radau systems

64%
Berriochoa E., Cachafeiro A., Díaz J., Martínez E.
Open Mathematics
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2016
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tom 14
|
nr 1
156-166
EN
This paper is devoted to Hermite interpolation with Chebyshev-Lobatto and Chebyshev-Radau nodal points. The aim of this piece of work is to establish the rate of convergence for some types of smooth functions. Although the rate of convergence is similar to that of Lagrange interpolation, taking into account the asymptotic constants that we obtain, the use of this method is justified and it is very suitable when we dispose of the appropriate information.
11
Content available remote

The best uniform quadratic approximation of circular arcs with high accuracy

64%
Rababah A.
Open Mathematics
|
2016
|
tom 14
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nr 1
118-127
EN
In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfy the properties of the best uniform approximation and yield the highest possible accuracy.
12
Content available remote

Local approximation properties of certain class of linear positive operators via I-convergence

64%
Özarslan M., Aktuǧlu H.
Open Mathematics
|
2008
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tom 6
|
nr 2
281-286
EN
In this study, we obtain a local approximation theorems for a certain family of positive linear operators via I-convergence by using the first and the second modulus of continuities and the elements of Lipschitz class functions. We also give an example to show that the classical Korovkin Theory does not work but the theory works in I-convergence sense.
13
Content available remote

I-convergence theorems for a class of k-positive linear operators

64%
Özarslan M.
Open Mathematics
|
2009
|
tom 7
|
nr 2
357-362
EN
In this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.
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