Blending type approximation by generalized Bernstein-Durrmeyer type operators

Kajla, Arun; Acar, Tuncer

doi:10.18514/mmn.2018.2216

Cited by 43 publications

(22 citation statements)

References 12 publications

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“…The motivation for this paper is the operator constructed in 2017 by Chen et al in [12] and it is a new family of generalized Bernstein operators depending on a nonnegative real parameter α . The α -Bernstein operators and their generalizations were extensively studied in last two years by many researchers, as we can see in [1][2][3][4][22][23][24].…”

Section: Construction Of the Generalized Bernstein-stancu Operators Amentioning

confidence: 99%

Approximation by generalized Bernstein–Stancu operators

Çetin¹,

Radu²

2019

Turk J Math

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In this paper, we investigate approximation properties of the Stancu type generalization of the α-Bernstein operator. We obtain a recurrence relation for moments and the rate of convergence by means of moduli of continuity. Also, we present Voronovskaya and Grüss-Voronovskaya type asymptotic results for these operators. Finally, the study contains numerical considerations regarding the constructed operators based on Maple algorithms.

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Section: Construction Of the Generalized Bernstein-stancu Operators Amentioning

confidence: 99%

Approximation by generalized Bernstein–Stancu operators

Çetin¹,

Radu²

2019

Turk J Math

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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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“…For θ = 1, it reduces to original Bernstein operators. Several types of such operators have been studied so far, for example, Kajla and Acar [4] gave the integral variant of the operators (1) and studied the approximation properties of these operators. Genuine Bernstein-Durrmeyer type operators were defined and studied in [5].…”

Section: Introductionmentioning

confidence: 99%

Durrmeyer-Type Generalization of Parametric Bernstein Operators

2020

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In this paper, we present a Durrmeyer type generalization of parametric Bernstein operators. Firstly, we study the approximation behaviour of these operators including a local and global approximation results and the rate of approximation for the Lipschitz type space. The Voronovskaja type asymptotic formula and the rate of convergence of functions with derivatives of bounded variation are established. Finally, the theoretical results are demonstrated by using MAPLE software.

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Blending type approximation by generalized Bernstein-Durrmeyer type operators

Cited by 43 publications

References 12 publications

Approximation by generalized Bernstein–Stancu operators

Approximation by generalized Bernstein–Stancu operators

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

Durrmeyer-Type Generalization of Parametric Bernstein Operators

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