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

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. Copyright (C) 2006 G. A. Anastassiou and S. G. Gal.