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Geometric and approximation properties of some singular integrals in the unit disk. (English) Zbl 1193.42075
Summary: 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.

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
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