IJPAM: Volume 80, No. 2 (2012)

CERTAIN SUBCLASS OF BOUNDED STARLIKE FUNCTIONS

Norlyda Mohamed$^1$, Daud Mohamad$^2$, Shaharuddin C. Soh$^3$
$^{1,2,3}$Department of Mathematics
Faculty of Computers and Mathematical Sciences
Universiti Teknologi MARA Malaysia
40450, Shah Alam Selangor, MALAYSIA


Abstract. Let $\mathcal{R}_{\alpha, \beta}{(\gamma, \delta)}$ be the subclass of normalized analytic functions f and satisfy Re ${e^{i\delta}\{{\alpha f'(z)+\beta z f''(z)}\}>\gamma}$ in the open unit disk $D=\{z\in \mathbb{C}:\vert z\vert<1\}$ for some $\alpha>0, \beta>0$ and $\gamma \in \mathbb{R} (0 \leq \gamma < \alpha)$ where $\alpha \cos \delta - \gamma > 0$. In this paper, we find the extreme points of $\mathcal{R}_{\alpha, \beta}{(\gamma, \delta)}$ and then obtain sharp bound for $a_{n}$ and bound for $f(z)$.

Received: May 9, 2012

AMS Subject Classification: 30C45

Key Words and Phrases: univalent functions, starlike functions, extreme points, coefficient estimates

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 80
Issue: 2