Szász-Durrmeyer Operators Based on Dunkl Analogue

Wafi, Abdul; Rao, Nadeem

doi:10.1007/s11785-017-0647-7

Cited by 17 publications

(12 citation statements)

References 10 publications

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“…Researchers have obtained several approximations of Szász-Mirakyan type operators via Dunkl generalization; for instance, see [6,18,26,28,29,32,39]. Related to these results, more approximation results have been studied in different functional spaces (see [1,2,4,5,14,38] and [3,16,27,31]).…”

Section: Introductionmentioning

confidence: 99%

Approximation on a class of Szász–Mirakyan operators via second kind of beta operators

et al. 2020

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In the present article, we construct a new sequence of positive linear operators via Dunkl analogue of modified Szász-Durrmeyer operators. We study the moments and basic results. Further, we investigate the pointwise approximation and uniform approximation results in various functional spaces for these sequences of positive linear operators. Finally, we prove the global approximation and A-statistical convergence results for these operators.

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Section: Introductionmentioning

confidence: 99%

Approximation on a class of Szász–Mirakyan operators via second kind of beta operators

et al. 2020

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“…Szász operators [20] provide an extension to Bernstein operators [4] on the interval [0, ∞). In the present years, several authors have studied the Dunkl type generalization of Szász operators (see [1,2,9,10,12,13,[15][16][17]21]).…”

Section: Preliminaries and Introductionmentioning

confidence: 99%

Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces

Mursaleen¹,

Nasiruzzaman²,

Kılıçman³

et al. 2020

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Purpose of this article is to introduce a modification of Phillips operators on the interval 1 2 , ∞ via Dunkl generalization. This type of modification enables to provide an error estimation on the interval 1 2 , ∞ . We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's K-functional and second order modulus of continuity.

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“…Szász operators [18] provide an extension to Bernstein operators [4] on the interval [0, ∞). In the present years, several authors have studied the Dunkl type generalization of Szász operators (see [1,2,[9][10][11][12][14][15][16]19]).…”

Section: Preliminaries and Introductionmentioning

confidence: 99%

Dunkl generalization of Phillips operators and approximation in weighted spaces

Mursaleen¹,

Nasiruzzaman²,

Kılıçman³

et al. 2019

Preprint

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Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2}% ,\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

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Szász-Durrmeyer Operators Based on Dunkl Analogue

Cited by 17 publications

References 10 publications

Approximation on a class of Szász–Mirakyan operators via second kind of beta operators

Approximation on a class of Szász–Mirakyan operators via second kind of beta operators

Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces

Dunkl generalization of Phillips operators and approximation in weighted spaces

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