Journal of the
Korean Mathematical Society JKMS

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

MSC numbers: 30E10, 30C45, 41A25, 41A35, 41A65