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http://dx.doi.org/10.4134/JKMS.2006.43.2.425

GEOMETRIC AND APPROXIMATION PROPERTIES OF GENERALIZED SINGULAR INTEGRALS IN THE UNIT DISK  

Anastassiou George A. (Department of Mathematical Sciences The University of Memphis)
Gal Sorin G. (Department of Mathematics University of Oradea)
Publication Information
Journal of the Korean Mathematical Society / v.43, no.2, 2006 , pp. 425-443 More about this Journal
Abstract
The aim of this paper is to obtain several results in approximation by Jackson-type generalizations of complex Picard, Poisson-Cauchy and Gauss-Weierstrass singular integrals in terms of higher order moduli of smoothness. In addition, these generalized integrals preserve some sufficient conditions for starlikeness and univalence of analytic functions. Also approximation results for vector-valued functions defined on the unit disk are given.
Keywords
generalized complex singular integrals; Jackson-type estimates; global smoothness preservation; shape preserving properties; approximation of vector-valued functions;
Citations & Related Records

Times Cited By Web Of Science : 3  (Related Records In Web of Science)
Times Cited By SCOPUS : 3
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