Approximation of functions by Stancu variant of Bernstein–Kantorovich operators based on shape parameter $${\varvec{\alpha }}$$

Mohiuddine, S. A.; Özger, Faruk

doi:10.1007/s13398-020-00802-w

Cited by 84 publications

(42 citation statements)

References 24 publications

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“…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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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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“…Several generalizations and modifications of these kinds of operators have been recently considered in previous studies 2–7 . Stancu 8 gave a class of positive and linear operators based on a nonnegative parameter α defined by the formula

P_{m}^{false[α false]} ((), ζ; x) = true \sum_{k = 0}^{m} b_{m, k}^{false[α false]} false(x false) ζ ((), \frac{k}{m}) = true \sum_{k = 0}^{m} ((), \binom{m}{k}) \frac{\prod_{ν = 0}^{k - 1} false(x + ν α false) \prod_{μ = 0}^{m - k - 1} false(1 - x + μ α false)}{false(1 + α false) false(1 + 2 α false) \dots false(1 + false(m - 1 false) α false)} ζ ((), \frac{k}{m})

for any

x \in ℐ

.…”

Section: Introductionmentioning

confidence: 99%

Blending‐type approximation by Lupaş–Durrmeyer‐type operators involving Pólya distribution

Kajla

Mohiuddine

Alotaibi

2021

Math Methods in App Sciences

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In the present work, we construct a new sequence of positive linear operatorsinvolving Pólya distribution. We compute a Voronovskaja type and a Grüss–Voronovskaja type asymptotic formula as well as the rate of approximation by using the modulus of smoothness and for functions in a Lipschitz type space. Lastly, we provide some numerical results, which explain the validity of the theoretical results and the effectiveness of the constructed operators.

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“…The q-analogues of Szász operators on the Dunkl type have been studied by several authors in [10][11][12] and for postquantum calculus in [9,[13][14][15]. We also refer some useful research articles on these topic (see [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]). Some convergence properties of operators through summability techniques can be examined in [34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Approximation of Functions by Dunkl-Type Generalization of Szász-Durrmeyer Operators Based on $(p, q)$ -Integers

Alotaibi

2021

Journal of Function Spaces

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In this article, our main purpose is to define the p , q -variant of Szász-Durrmeyer type operators with the help of Dunkl generalization generated by an exponential function. We estimate moments and establish some direct results of the aforementioned operators. Moreover, we establish some approximation results in weighted spaces.

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Approximation of functions by Stancu variant of Bernstein–Kantorovich operators based on shape parameter $${\varvec{\alpha }}$$

Cited by 84 publications

References 24 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

Blending‐type approximation by Lupaş–Durrmeyer‐type operators involving Pólya distribution

Approximation of Functions by Dunkl-Type Generalization of Szász-Durrmeyer Operators Based on $(p, q)$ -Integers

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Approximation of functions by Stancu variant of Bernstein–Kantorovich operators based on shape parameter $${\varvec{\alpha }}$$

Cited by 84 publications

References 24 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

Blending‐type approximation by Lupaş–Durrmeyer‐type operators involving Pólya distribution

Approximation of Functions by Dunkl-Type Generalization of Szász-Durrmeyer Operators Based on p , q -Integers

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Approximation of Functions by Dunkl-Type Generalization of Szász-Durrmeyer Operators Based on $(p, q)$ -Integers