Abstract.
In this paper, firstly we prove the Voronovskaja’s convergence theorem for complex Bernstein polynomials in compact disks in \({\mathbb{C}}\), centered at origin, with quantitative estimates of this convergence. Secondly, we study the approximation properties of the iterates of complex Bernstein polynomials and we prove that they preserve in the unit disk (beginning with an index) the univalence, starlikeness, convexity and spirallikeness.
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This work was supported by the Romanian Ministry of Education and Research, under CEEX grant, code 2-CEx 06-11-96.
Received: May 5, 2007 Revised: September 14, 2007 and November 11, 2007 Accepted: November 26, 2007
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Gal, S.G. Voronovskaja’s Theorem and Iterations for Complex Bernstein Polynomials in Compact Disks. MedJM 5, 253–272 (2008). https://doi.org/10.1007/s00009-008-0148-z
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DOI: https://doi.org/10.1007/s00009-008-0148-z