A class of univalent functions defined by a differential inequality

Kodai Mathematical Journal

Saminathan Ponnusamy¹  Milutin Obradović² 

[1] Department of Mathematics Indian Institute of Technology Madras;Department of Mathematics Faculty of Civil Engineering University of Belgrade

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

DOI  :  10.2996/kmj/1309829544

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(10)Let $\mathcal{A}$ be the class of analytic functions in the unit disk D with the normalization f(0) = f′(0) − 1 = 0. For λ > 0, denote by $\mathcal{M}$(λ) the class of functions f ∈ $\mathcal{A}$ which satisfy the condition$$\left |z^2\left (\frac{z}{f(z)}\right )''+ f'(z)\left(\frac{z}{f(z)} \right)^{2}-1\right |\leq \lambda,\quad z\in \mathbf{D}.$$We show that functions in $\mathcal{M}$(1) are univalent in D and we present one parameter family of functions in $\mathcal{M}$(1) that are also starlike in D. In addition to certain inclusion results, we also present characterization formula, necessary and sufficient coefficient conditions for functions in $\mathcal{M}$(λ), and a radius property of $\mathcal{M}$(1).

【 授权许可】

Unknown