For n ≥ 1, let denote the class of all analytic functions f in the unit disk Δ of the form . For Re α < 2 and γ > 0 given, let (γ,α) denote the class of all functions f ∈ satisfying the condition |f’(z) - α f(z)/z + α - 1| ≤ γ, z ∈ Δ. We find sufficient conditions for functions in (γ,α) to be starlike of order β. A generalization of this result along with some convolution results is also obtained.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-3-7,
author = {S. Ponnusamy and P. Vasundhra},
title = {Sufficient conditions for starlike and convex functions},
journal = {Annales Polonici Mathematici},
volume = {92},
year = {2007},
pages = {277-288},
zbl = {1127.30007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-3-7}
}
S. Ponnusamy; P. Vasundhra. Sufficient conditions for starlike and convex functions. Annales Polonici Mathematici, Tome 92 (2007) pp. 277-288. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-3-7/