A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices

Srivástava, H. M.; Ansari, Khursheed J.; Özger, Faruk; Özger, Zeynep Ödemiş

doi:10.3390/math9161895

Cited by 36 publications

(15 citation statements)

References 38 publications

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“…The shape-preserving properties of this operator are also given by them. Srivastava et al [29] established a link between approximation theory and summability methods by constructing bivariate Bernstein-Kantorovich type operators on an extended domain with re-parameterized knots. They numerically analyzed the theoretical results and gave some computer graphics to understand the importance of this study.…”

Section: Introductionmentioning

confidence: 99%

A Novel Generalization of Bézier-like Curves and Surfaces with Shape Parameters

et al. 2022

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Bézier curves and surfaces with shape parameters have received more attention in the field of engineering and technology in recent years because of their useful geometric properties as compared to classical Bézier curves, as well as traditional Bernstein basis functions. In this study, the generalized Bézier-like curves (gBC) are constructed based on new generalized Bernstein-like basis functions (gBBF) with two shape parameters. The geometric properties of both gBBF and gBC are studied, and it is found that they are similar to the classical Bernstein basis and Bézier curve, respectively. Some free form curves can be modeled using the proposed gBC and surfaces as the applications.

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Section: Introductionmentioning

confidence: 99%

A Novel Generalization of Bézier-like Curves and Surfaces with Shape Parameters

et al. 2022

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“…For the operators defined by (4), they studied some theorems such as Korovkin type convergence, local approximation, Lipschitz type convergence, Voronovskaja and Grüss-Voronovskaja type. Also, we refer some recent works based on shape parameter λ ∈ [−1, 1], see details: [5,6,8,[19][20][21][22][23][24][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Approximation by Szasz-Mirakjan-Durrmeyer operators based on shape parameter $\lambda$

Aslan

2022

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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In this paper, we study several approximation properties of Szasz-Mirakjan-Durrmeyer operators with shape parameter λ∈[−1,1]λ∈[−1,1]. Firstly, we obtain some preliminaries results such as moments and central moments. Next, we estimate the order of convergence in terms of the usual modulus of continuity, for the functions belong to Lipschitz type class and Peetre's K-functional, respectively. Also, we prove a Korovkin type approximation theorem on weighted spaces and derive a Voronovskaya type asymptotic theorem for these operators. Finally, we give the comparison of the convergence of these newly defined operators to the certain functions with some graphics and error of approximation table.

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“…In the year 2020, Mursaleen et al [21] considered Chlodowsky kind (λ, q)-Bernstein-Stancu polynomials and derived Korovkin-type convergence, and Voronovskaya-type asymptotic theorems. For some recent relevant works we refer to [22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Note on a New Construction of Kantorovich Form q-Bernstein Operators Related to Shape Parameter λ

Cai¹,

Aslan²

2022

Computer Modeling in Engineering &Amp; Sciences

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The main purpose of this paper is to introduce some approximation properties of a Kantorovich kind q-Bernstein operators related to Bézier basis functions with shape parameter λ ∈ [−1, 1]. Firstly, we compute some basic results such as moments and central moments, and derive the Korovkin type approximation theorem for these operators. Next, we estimate the order of convergence in terms of the usual modulus of continuity, for the functions belong to Lipschitz-type class and Peetre's K-functional, respectively. Lastly, with the aid of Maple software, we present the comparison of the convergence of these newly defined operators to the certain function with some graphical illustrations and error estimation table.

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A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices

Cited by 36 publications

References 38 publications

A Novel Generalization of Bézier-like Curves and Surfaces with Shape Parameters

A Novel Generalization of Bézier-like Curves and Surfaces with Shape Parameters

Approximation by Szasz-Mirakjan-Durrmeyer operators based on shape parameter $\lambda$

Note on a New Construction of Kantorovich Form q-Bernstein Operators Related to Shape Parameter λ

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