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Journals / Gazi University Journal of Science / 2025 / Volume: 38 Issue: 4

Complex Perturbed Bernstein-Schurer-Type Operators

Nursel Çetin(ANKARA HACI BAYRAM VELI UNIVERSITY)0000-0003-3771-6523
Pages
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Publication Date
2025-12-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We attain quantitative upper estimates for the convergence, lower estimates from a qualitative Voronovskaya type result and afterwards establish the exact degree of simultaneous approximation by the specified operator attached to analytical functions in a disk centered at the origin having radius greater than one.

📌 3 Key Takeaways

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Objective & Hypothesis:In the present paper, we describe a new generalization of complex Bernstein-Schurer operators.
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Key Findings & Data:In the present paper, we describe a new generalization of complex Bernstein-Schurer operators.
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Conclusion & Impact:We attain quantitative upper estimates for the convergence, lower estimates from a qualitative Voronovskaya type result and afterwards establish the exact degree of simultaneous approximation by the specified operator attached to analytical functions in a disk centered at the origin having radius greater than one.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Perturbed Bernstein operator · Complex Bernstein-Schurer operator · Simultaneous approximation

Abstract

In the present paper, we describe a new generalization of complex Bernstein-Schurer operators. We attain quantitative upper estimates for the convergence, lower estimates from a qualitative Voronovskaya type result and afterwards establish the exact degree of simultaneous approximation by the specified operator attached to analytical functions in a disk centered at the origin having radius greater than one.

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Cite This Article

Çetin, N. (2025). Complex Perturbed Bernstein-Schurer-Type Operators. Gazi University Journal of Science, Volume: 38 Issue: 4. https://doi.org/10.35378/gujs.1598374

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References (14)

  1. Anastassiou, G.A., Gal, S.G., “Approximation by complex Bernstein-Schurer and Kantorovich-Schurer polynomials in compact disks”, Computers and Mathematics with Applications, 58: 734–743, (2009). DOI: https://doi.org/10.1016/j.camwa.2009.04.009
  2. Gal, S.G., Approximation by Complex Bernstein and Convolution Type Operators, Series on Concrete and Applicable Mathematics, vol. 8. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 1–336, (2009).
  3. Dzyadyk, V.K., Shevchuk, I.A., Theory of uniform approximation of functions by polynomials, Walter de Gruyter GmbH & Co. KG, Berlin, 1–437, (2008).
  4. Çetin, N., “A new complex generalized Bernstein-Schurer operator”, Carpathian Journal of Mathematics, 37(1): 81–89, (2021). DOI: https://doi.org/10.37193/CJM.2021.01.08
  5. Khosravian-Arab, H., Dehghan, M., Eslahchi, M.R., “A new approach to improve the order of approximation of the Bernstein operators: Theory and applications”, Numerical Algorithms, 77(1): 111–150, (2018). DOI: https://doi.org/10.1007/s11075-017-0307-z
  6. Acu, A.M., Gupta, V., Tachev, G., “Better numerical approximation by Durrmeyer type operators”, Results in Mathematics, 74: 90, (2019). DOI: https://doi.org/10.1007/s00025-019-1019-6
  7. Acu, A.M., Gonska, H., “Perturbed Bernstein-type operators”, Analysis and Mathematical Physics, 10: 49, (2020). DOI: https://doi.org/10.1007/s13324-020-00389-w
  8. Acu, A.M., Başcanbaz-Tunca, G., Çetin, N., “Approximation by certain linking operators”, Annals of Functional Analysis, 11: 1184–1202, (2020). DOI: https://doi.org/10.1007/s43034-020-00081-x
  9. Acu, A.M., Başcanbaz-Tunca, G., “Approximation by complex perturbed Bernstein-type operators”, Results in Mathematics, 75: 120, (2020). DOI: https://doi.org/10.1007/s00025-020-01244-x
  10. Acu, A.M., Çetin, N., Tachev, G., “Approximation by perturbed Baskakov-type operators”, Journal of Mathematical Inequalities, 18(2): 551–563, (2024). DOI: https//doi.org/10.7153/jmi-2024-18-30
  11. Acu, A.M., Mutlu, G., Çekim, B., Yazıcı, S., “A new representation and shape preserving properties of perturbed Bernstein operators”, Mathematical Methods in the Applied Sciences, 47(1): 5–14, (2024). DOI: https://doi.org/10.1002/mma.9636
  12. Çetin, N., “On complex modified Bernstein-Stancu operators”, Mathematical Foundations of Computing, 6(1): 63–77, (2023). DOI: https://doi.org/10.3934/mfc.2021043
  13. Çetin, N., “Approximation by α-Bernstein-Schurer operator”, Hacettepe Journal of Mathematics & Statistics, 50(3): 732–743, (2021). DOI: https://doi.org/10.15672/hujms.626905
  14. Bărbosu, D., Bărbosu, M., “Simultaneous approximation by Schurer type operators”, Carpathian Journal of Mathematics, 19(1): 1–6, (2003).