The radius of starlikeness for polynomial mappings and finite Blaschke products with zeroes distributed at equal angles around a circle centered at the origin, as well as with zeroes concentrated at a single point, are considered, and sharp bounds are obtained. Results expressing the radius of starlikeness of an arbitrary polynomial or Blaschke product in terms of the magnitudes of the zeroes are also given. These are also sharp.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-2-7,
author = {Alan Gluchoff and Frederick Hartmann},
title = {Starlikeness of polynomials and finite Blaschke products},
journal = {Annales Polonici Mathematici},
volume = {93},
year = {2008},
pages = {187-196},
zbl = {1135.30011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-2-7}
}
Alan Gluchoff; Frederick Hartmann. Starlikeness of polynomials and finite Blaschke products. Annales Polonici Mathematici, Tome 93 (2008) pp. 187-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-2-7/