Geometric and approximate properties of convolution polynomials in the unit disk
by
S. G. Gal
Vol. 1 No. 2 (2006) P.307~P.336
ABSTRACT
The purpose of this paper is to prove several results in approximations through complex convolution polynomials with Jackson-type rate or with best approximation rate, having the quality of preservation of some properties in geometric function theory, like the preservation of: coecients' bounds, positive real part, bounded turn, close-to-convexity, starlikeness, convexity, spi-
rallikeness, $\alpha$-convexity. Also, some sucient conditions for star-likeness and univalence of analytic functions are preserved.
KEYWORDS
Convolution-type complex polynomials, Jackson-type esti- mates, Beatson kernels, shape preserving properties
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 30E10, 30C45, 30C50, 30C55, 42A10, 41A25
MILESTONES
Received: 2004-02-13
Revised : 2004-06-12
Accepted:
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