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Mediterranean Journal of Mathematics

, Volume 5, Issue 3, pp 253–272 | Cite as

Voronovskaja’s Theorem and Iterations for Complex Bernstein Polynomials in Compact Disks

  • Sorin G. Gal
Article

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.

Mathematics Subject Classification (2000).

Primary 30E10 Secondary 30C10, 30C45 

Keywords.

Complex Bernstein polynomials Voronovskaja’s theorem iterates univalence starlikeness convexity and spirallikeness 

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Copyright information

© Birkhaueser 2008

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of OradeaOradeaRomania

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