Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 17231, 19 pages
doi:10.1155/JIA/2006/17231
Geometric and approximation properties of some singular integrals in the unit disk
1Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA
2Department of Mathematics, University of Oradea, Str. Armatei Romane 5, Oradea 410087, Romania
Received 23 January 2006; Revised 19 April 2006; Accepted 20 April 2006
Copyright © 2006 George A. Anastassiou and Sorin G. Gal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.