Coefficient inequalities for concave and meromorphically starlike univalent functions

B. Bhowmik, and S. Ponnusamy. "Coefficient inequalities for concave and meromorphically starlike univalent functions." Annales Polonici Mathematici 93.2 (2008): 177-186. <http://eudml.org/doc/280395>.

@article{B2008,
abstract = {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 $f(z) = ∑_\{n=-1\}^\{∞\} aₙ(z-p)ⁿ$, |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 $Co(p)(Σ^\{s\}(p,w₀)$ resp.). We prove some coefficient estimates for functions in these classes; the sharpness of these estimates is also established.},
author = {B. Bhowmik, S. Ponnusamy},
journal = {Annales Polonici Mathematici},
keywords = {Laurent coefficients; meromorphic univalent functions; concave functions; starlike functions; convex set},
language = {eng},
number = {2},
pages = {177-186},
title = {Coefficient inequalities for concave and meromorphically starlike univalent functions},
url = {http://eudml.org/doc/280395},
volume = {93},
year = {2008},
}

TY - JOUR
AU - B. Bhowmik
AU - S. Ponnusamy
TI - Coefficient inequalities for concave and meromorphically starlike univalent functions
JO - Annales Polonici Mathematici
PY - 2008
VL - 93
IS - 2
SP - 177
EP - 186
AB - 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 $f(z) = ∑_{n=-1}^{∞} aₙ(z-p)ⁿ$, |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 $Co(p)(Σ^{s}(p,w₀)$ resp.). We prove some coefficient estimates for functions in these classes; the sharpness of these estimates is also established.
LA - eng
KW - Laurent coefficients; meromorphic univalent functions; concave functions; starlike functions; convex set
UR - http://eudml.org/doc/280395
ER -