Coefficient inequalities for univalent starlike functions

Mathematica Slovaca

Milutin Obradović¹  Saminathan Ponnusamy¹ 

关键词: coefficient inequality;    analytic;    Hadamard convolution;    univalent and starlike functions;   

DOI  :  10.2478/s12175-013-0159-5

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

Let A be the class of analytic functions in the unit disk $$mathbb{D}$$ with the normalization f(0) = f′(0) − 1 = 0. In this paper the authors discuss necessary and sufficient coefficient conditions for f ∈ A of the form $$left( {frac{z}{{f(z)}}} ight)^mu = 1 + b_1 z + b_2 z^2 + ldots$$ to be starlike in $$mathbb{D}$$ and more generally, starlike of some order β, 0 ≤ β < 1. Here µ is a suitable complex number so that the right hand side expression is analytic in $$mathbb{D}$$ and the power is chosen to be the principal power. A similar problem for the class of convex functions of order β is open.

【 授权许可】

Unknown