Some approximation results for (p,q)-Lupaş-Schurer operators

Kanat, Kadir; Sofyalıoğlu, Melek

doi:10.2298/fil1801217k

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…A new type -Bernstein operators have been introduced by Cai et al in [6] based on Bézier bases de…ned by Ye et al in [30]. We refer to [5,6,20,23,26] for recent studies about -Bernstein type operators and [13,14,28] for some Schuer type operators.…”

Section: -Schurer Operators and Corresponding Results In Approximatiomentioning

confidence: 99%

On new Bézier bases with Schurer polynomials and corresponding results in approximation theory

Özger

2019

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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A new type Bézier bases with shape parameters have been de-…ned [30, Ye et al., 2010]. We slightly modify these bases to establish new Bézier bases with Schurer polynomials and shape parameters. We construct a new type Schurer operators via de…ned new Bézier-Schurer bases. Also, we study statistical convergence properties of these operators and obtain an estimate for the rate of weighted A-statistical convergence. Moreover, we prove two Voronovskaja-type theorems including a Voronovskaja-type approximation theorem using weighted A-statistical convergence.

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Section: -Schurer Operators and Corresponding Results In Approximatiomentioning

confidence: 99%

On new Bézier bases with Schurer polynomials and corresponding results in approximation theory

Özger

2019

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…1 for several values of m by using Algorithm 2 . Furthermore, we give the error estimates in Table 2 in order to indicate that the -analogue Lupaş–Schurer operators [ 14 ] converge and then plot Fig. 2 .…”

Section: Graphical Illustrationsmentioning

confidence: 99%

Approximation by ( p , q ) $(p,q)$ -Lupaş–Schurer–Kantorovich operators

Kanat

Sofyalıoğlu

2018

J Inequal Appl

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In the current paper, we examine the -analogue of Kantorovich type Lupaş–Schurer operators with the help of -Jackson integral. Then, we estimate the rate of convergence for the constructed operators by using the modulus of continuity in terms of a Lipschitz class function and by means of Peetre’s K-functionals based on Korovkin theorem. Moreover, we illustrate the approximation of the -Lupaş–Schurer–Kantorovich operators to appointed functions by the help of Matlab algorithm and then show the comparison of the convergence of these operators with Lupaş–Schurer operators based on -integers.

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“…Firstly, Mursaleen et al carried this concept to the approximation theory [7]. After then, (𝑝, 𝑞)operators have been studied by different authors for examples [8][9][10][11][12][13][14][15][16][17]. Karaisa [18] defined bivariate form of (𝑝, 𝑞)-Bernstein operators.…”

Section: Introductionmentioning

confidence: 99%