q-Szász–Durrmeyer Type Operators Based on Dunkl Analogue

Rao, Nadeem; Wafi, Abdul; Acu, Ana Maria

doi:10.1007/s11785-018-0816-3

Cited by 27 publications

(13 citation statements)

References 12 publications

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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%

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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%

“…For more related results on (p, q)-analogues, we refer to [1-6, 8, 9, 11, 14-21, 26, 30, 43, 44, 48] and also see [12,32,40], for example, if p = 1, the operators P τ s,p,q reduce to those considered recently (see [45]). We have the following inequalities.…”

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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“…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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“…The (p, q)and q-Dunkl analogues have been studied by several authors (see [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]). For the most recent work on (p, q)-approximation, we refer to [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

A Dunkl–Type Generalization of Szász–Kantorovich Operators via Post–Quantum Calculus

2019

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In this paper, we define the ( p , q ) -variant of Szász–Kantorovich operators via Dunkl-type generalization generated by an exponential function and study the Korovkin-type results. We also obtain the convergence of our operators in weighted space by the modulus of continuity, Lipschitz class, and Peetre’s K-functionals. The extra parameter p provides more flexibility in approximation and plays an important role in symmetrizing these newly-defined operators.

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q-Szász–Durrmeyer Type Operators Based on Dunkl Analogue

Cited by 27 publications

References 12 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

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

A Dunkl–Type Generalization of Szász–Kantorovich Operators via Post–Quantum Calculus

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