Stancu Type Baskakov—Durrmeyer Operators and Approximation Properties

Kılıçman, Adem; Mursaleen, Mohammad Ayman; Al-Abied, Ahmed Ahmed Hussin Ali

doi:10.3390/math8071164

Cited by 25 publications

(16 citation statements)

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“…In this section we construct a class of (p, q)-variant of Szász-Beta operators of the second kind generated by an exponential function via Dunkl generalization in Definition 2.1. Such operators are a generalized version of the operators studied in [7,22,28,29,31,36,45].…”

Section: Operators and Basic Estimatesmentioning

confidence: 99%

Dunkl-type generalization of the second kind beta operators via $(p,q)$-calculus

2021

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The main purpose of this research article is to construct a Dunkl extension of $(p,q)$ ( p , q ) -variant of Szász–Beta operators of the second kind by applying a new parameter. We obtain Korovkin-type approximation theorems, local approximations, and weighted approximations. Further, we study the rate of convergence by using the modulus of continuity, Lipschitz class and Peetre’s K-functionals.

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Section: Operators and Basic Estimatesmentioning

confidence: 99%

Dunkl-type generalization of the second kind beta operators via $(p,q)$-calculus

2021

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“…Numerous mathematicians dealt with the extension of these operators. For example, operators including generalized Appell polynomials [7], Stancu type Baskakov-Durrmeyer operators [10], Stancu type Dunkl generalization of Szász-Kantorovich operators [13].…”

Section: Introductionmentioning

confidence: 99%

Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators

2021

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In this article, we establish the approximation by Durrmeyer type Jakimovski–Leviatan operators involving the Brenke type polynomials. The positive linear operators are constructed for the Brenke polynomials, and thus approximation properties for these polynomials are obtained. The order of convergence and the weighted approximation are also considered. Finally, the Voronovskaya type theorem is demonstrated for some particular case of these polynomials.

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“…The accuracy of the approximation is also illustrated by graphics of given functions with suitable Bernstein-type approximation. For more information regarding such operators, their properties and their remainders one can refer to [15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”

Section: Introduction and Essential Preliminariesmentioning

confidence: 99%

Phillips-Type $q$ -Bernstein Operators on Triangles

Khan

Mansoori

Khan³

et al. 2021

Journal of Function Spaces

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The purpose of the paper is to introduce a new analogue of Phillips-type Bernstein operators B m , q u f u , v and B n , q v f u , v , their products P m n , q f u , v and Q n m , q f u , v , their Boolean sums S m n , q f u , v and T n m , q f u , v on triangle T h , which interpolate a given function on the edges, respectively, at the vertices of triangle using quantum analogue. Based on Peano’s theorem and using modulus of continuity, the remainders of the approximation formula of corresponding operators are evaluated. Graphical representations are added to demonstrate consistency to theoretical findings. It has been shown that parameter q provides flexibility for approximation and reduces to its classical case for q = 1 .

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Stancu Type Baskakov—Durrmeyer Operators and Approximation Properties

Abstract: In this article, we introduce Stancu type generalization of Baskakov–Durrmeyer operators by using inverse Pólya–Eggenberger distribution. We discuss some basic results and approximation properties. Moreover, we study the statistical convergence for these operators.

Cited by 25 publications

References 9 publications

Dunkl-type generalization of the second kind beta operators via $(p,q)$-calculus

Dunkl-type generalization of the second kind beta operators via $(p,q)$-calculus

Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators

Phillips-Type $q$ -Bernstein Operators on Triangles

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Stancu Type Baskakov—Durrmeyer Operators and Approximation Properties

Abstract: In this article, we introduce Stancu type generalization of Baskakov–Durrmeyer operators by using inverse Pólya–Eggenberger distribution. We discuss some basic results and approximation properties. Moreover, we study the statistical convergence for these operators.

Cited by 25 publications

References 9 publications

Dunkl-type generalization of the second kind beta operators via $(p,q)$-calculus

Dunkl-type generalization of the second kind beta operators via $(p,q)$-calculus

Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators

Phillips-Type q -Bernstein Operators on Triangles

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Product

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Phillips-Type $q$ -Bernstein Operators on Triangles