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Geometric and approximation properties of some singular integrals in the unit disk

Abstract

The purpose of this paper is to prove several results in approximation by complex Picard, Poisson-Cauchy, and Gauss-Weierstrass singular integrals with Jackson-type rate, having the quality of preservation of some properties in geometric function theory, like the preservation of coefficients' bounds, positive real part, bounded turn, starlikeness, and convexity. Also, some sufficient conditions for starlikeness and univalence of analytic functions are preserved.

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Correspondence to George A. Anastassiou.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Anastassiou, G.A., Gal, S.G. Geometric and approximation properties of some singular integrals in the unit disk. J Inequal Appl 2006, 17231 (2006). https://doi.org/10.1155/JIA/2006/17231

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Keywords

  • Analytic Function
  • Unit Disk
  • Function Theory
  • Approximation Property
  • Singular Integral