The method of convolution is used to determine a sharp condition for starlikeness of analytic functions defined in the unit disc U = {z ∈ ℂ: |z| < 1} and having the property f(0) = f'(0) - 1 = 0. The integral version is given using the Alexander integral operator.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-1-1,
author = {R\'obert Sz\'asz},
title = {The sharp version of a criterion for starlikeness related to the operator of Alexander},
journal = {Annales Polonici Mathematici},
volume = {93},
year = {2008},
pages = {1-14},
zbl = {1187.30023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-1-1}
}
Róbert Szász. The sharp version of a criterion for starlikeness related to the operator of Alexander. Annales Polonici Mathematici, Tome 93 (2008) pp. 1-14. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-1-1/