Let denote the open unit disk and f: → ℂ̅ be meromorphic and univalent in with a simple pole at p ∈ (0,1) and satisfying the standard normalization f(0) = f’(0)-1 = 0. Also, assume that f has the expansion , |z-p| < 1-p, and maps onto a domain whose complement with respect to ℂ̅ is a convex set (starlike set with respect to a point w₀ ∈ ℂ, w₀ ≠ 0 resp.). We call such functions concave (meromorphically starlike resp.) univalent functions and denote this class by resp.). We prove some coefficient estimates for functions in these classes; the sharpness of these estimates is also established.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-2-6,
author = {B. Bhowmik and S. Ponnusamy},
title = {Coefficient inequalities for concave and meromorphically starlike univalent functions},
journal = {Annales Polonici Mathematici},
volume = {93},
year = {2008},
pages = {177-186},
zbl = {1135.30010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-2-6}
}
B. Bhowmik; S. Ponnusamy. Coefficient inequalities for concave and meromorphically starlike univalent functions. Annales Polonici Mathematici, Tome 93 (2008) pp. 177-186. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-2-6/