TY - JOUR T1 - Complex Perturbed Bernstein-Schurer-Type Operators AU - Çetin, Nursel PY - 2025 DA - December Y2 - 2025 DO - 10.35378/gujs.1598374 JF - Gazi University Journal of Science PB - Gazi University WT - DergiPark SN - 2147-1762 SP - 2065 EP - 2077 VL - 38 IS - 4 LA - en AB - 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. KW - Perturbed Bernstein operator KW - Complex Bernstein-Schurer operator KW - Simultaneous approximation KW - Equivalence CR - [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 CR - [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). CR - [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). CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [14] Bărbosu, D., Bărbosu, M., “Simultaneous approximation by Schurer type operators”, Carpathian Journal of Mathematics, 19(1): 1–6, (2003). UR - https://doi.org/10.35378/gujs.1598374 L1 - https://dergipark.org.tr/en/download/article-file/4426114 ER -