Approximation properties for the genuine modified Bernstein-Durrmeyer-Stancu operators

Cai, Qing-Bo; Kantar, Ülkü Dinlemez; Çekіm, Bayram

doi:10.1007/s11766-020-3918-y

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…Several studies were conducted on Voronovskaja type approximation for some operators by Dinlemez Kantar and Ergelen (2019), Cai et al (2020;2021a, 2021b, Sofyalıoğlu et al (2021), Dinlemez Kantar and Yüksel (2022), Torun et al (2022).…”

Section: Introductionmentioning

confidence: 99%

On Approximation Properties of Stancu Type Post-Widder Operators Preserving Exponential Functions

Torun

2022

Gazi University Journal of Science Part A: Engineering and Innovation

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In this article, Stancu type Post-Widder operators are introduced, which are a modification of the Post-Widder operators that preserve the functions constant and e^2ax for fixed a>0. The uniform convergence of these modified operators for the function f on [0,∞) is examined and then the convergence rate is investigated with the help of the continuity module. The Voronovskaja type asymptotic formula is obtained to examine the asymptotic behavior of these operators. Finally, numerical examples and graphs are given to show the convergence of Stancu type Post- Widder operators and compared with Post Widder operators.

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Section: Introductionmentioning

confidence: 99%

On Approximation Properties of Stancu Type Post-Widder Operators Preserving Exponential Functions

Torun

2022

Gazi University Journal of Science Part A: Engineering and Innovation

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“…where b λ,ν (χ) = ( λ ν )χ ν (1 − χ) λ−ν , ν = 0, 1, • • • , λ, ∈ C S . Later, many generalizations and modifications of these kinds of operators (1) have been constructed and considered, we refer the readers to these papers (see λ-Bernstein operators [2], generalized Bernstein operators [3,4], blending-type Bernstein operators [5][6][7], Durrmeyer-type Bernstein operators [8], genuine-type Bernstein operators [9,10], and so on).…”

Section: Introductionmentioning

confidence: 99%

Approximation Properties of the Blending-Type Bernstein–Durrmeyer Operators

Liu

Cheng

Zhang

et al. 2022

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We construct the blending-type modified Bernstein–Durrmeyer operators and investigate their approximation properties. First, we derive the Voronovskaya-type asymptotic theorem for this type of operator. Then, the local and global approximation theorems are obtained by using the classical modulus of continuity and K-functional. Finally, we derive the rate of convergence for functions with a derivative of bounded variation. The results show that the new operators have good approximation properties.

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“…(11)−(14) and choosing 𝑀𝑀 8 = 𝑀𝑀 1 𝑀𝑀 6 + 𝑀𝑀 3 𝑀𝑀 7 + 𝑀𝑀 5 where 𝑀𝑀 6 = 𝑠𝑠𝑠𝑠𝑠𝑠 𝑛𝑛≥0 1+𝑛𝑛 𝑀𝑀 7 = 𝑠𝑠𝑠𝑠𝑠𝑠 𝑛𝑛≥0 choosing 𝑀𝑀 = 𝑀𝑀 8 𝑀𝑀 9 where 𝑀𝑀 9 then combining the estimate between (9) and (14), we end up with the result of �𝐺𝐺 𝑛𝑛,𝑐𝑐 𝛼𝛼 (𝑓𝑓(𝑡𝑡) − 𝑓𝑓(𝑥𝑥); 𝑥𝑥)� ≤ 𝑀𝑀(1 + 𝑥𝑥 5 )𝛺𝛺 �𝑓𝑓, 1 √𝑛𝑛 �.…”

mentioning

confidence: 99%

Parametric Extension of a Certain Family of Summation-Integral Type Operators

Odabaşı,

Yüksel

2023

Cumhuriyet Science Journal

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In this paper, we introduce a parametric extension of a certain family of summation-integral type operators on the interval [0,∞). Firstly, we obtain test functions and central moments. Secondly, we investigate weighted approximation properties for these operators and estimate the rate of convergence. Then, we give a pointwise approximation for the Peetre K-functional and functions of the Lipschitz class. Moreover, we demonstrate Voronovskaja type theorem for the operators. Finally, the convergence properties of operators to some functions are illustrated by graphics.

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Approximation properties for the genuine modified Bernstein-Durrmeyer-Stancu operators

Cited by 4 publications

References 19 publications

On Approximation Properties of Stancu Type Post-Widder Operators Preserving Exponential Functions

On Approximation Properties of Stancu Type Post-Widder Operators Preserving Exponential Functions

Approximation Properties of the Blending-Type Bernstein–Durrmeyer Operators

Parametric Extension of a Certain Family of Summation-Integral Type Operators

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