Open Access

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

Journal of Inequalities and Applications20062006:17231

Received: 23 January 2006

Accepted: 20 April 2006

Published: 31 August 2006


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.


Authors’ Affiliations

Department of Mathematical Sciences, University of Memphis
Department of Mathematics, University of Oradea


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© Anastassiou and Gal 2006

This article is published under license to BioMed Central Ltd. 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.