A new generalization of complex Stancu operators

Çetin, Nursel

doi:10.1002/mma.5622

Cited by 4 publications

(2 citation statements)

References 12 publications

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“…Also, he prove that complex Bernstein operators preserve the univalence, starlikeness, convexity, and spirallikeness in the unit disk. After that, the problem of approximation of complex operators has attracted the attention of many researchers (see, e.g., [2,7,8]).…”

Section: Introduction the Classical Bernstein Polynomialsmentioning

confidence: 99%

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On complex modified Bernstein-Stancu operators

Çetin¹

2023

MFC

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<p style='text-indent:20px;'>The present paper deals with complex form of a generalization of perturbed Bernstein-type operators. Quantitative upper estimates for simultaneous approximation, a qualitative Voronovskaja type result and the exact order of approximation by these operators attached to functions analytic in a disk centered at the origin with radius greater than 1 are obtained in this study.</p>

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Section: Introduction the Classical Bernstein Polynomialsmentioning

confidence: 99%

“…from which we have the analogous representation of the complex Bernstein-Stancu operators in (7) when…”

Section: Introduction the Classical Bernstein Polynomialsmentioning

confidence: 99%

On complex modified Bernstein-Stancu operators

Çetin¹

2023

MFC

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Complex Generalized Stancu-Schurer Operators

Çetin,

Mutlu

2024

Mathematica Slovaca

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In the present study, we determine a Schurer type of complex generalized Stancu operators and examine its some approximation properties. Firstly, we obtain upper quantitative estimates for the convergence and then we get lower estimates from a qualitative Voronovskaja-type result for these specified operators attached to the analytic functions in an open disk centered at the origin. Hence, we present the exact order of simultaneous approximation by using obtained upper and lower estimates.

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On Stancu operators depending on a non-negative integer

Bostancı

Başcanbaz‐Tunca

2022

Filomat

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In this paper, we deal with Stancu operators which depend on a non-negative integer parameter. Firstly, we define Kantorovich extension of the operators. For functions belonging to the space Lp [0, 1] , 1 ? p < ?, we obtain convergence in the norm of Lp by the sequence of Stancu-Kantorovich operators, and we give an estimate for the rate of the convergence via first order averaged modulus of smoothness. Moreover, for the Stancu operators; we search variation detracting property and convergence in the space of functions of bounded variation in the variation seminorm.

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A new generalization of complex Stancu operators

Cited by 4 publications

References 12 publications

On complex modified Bernstein-Stancu operators

On complex modified Bernstein-Stancu operators

Complex Generalized Stancu-Schurer Operators

On Stancu operators depending on a non-negative integer

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