IJPAM: Volume 83, No. 2 (2013)

COEFFICIENT BOUND OF A GENERALIZED
CLOSE-TO-CONVEX FUNCTION

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


Abstract. We look at function $f(z)=z+\sum_{n=2}^{\infty} a_{n} z^n$, which are analytic in the unit disc $E=\{z:\vert z\vert<1\}$. For$\vert\alpha\vert<\pi$ and $\cos \alpha > \delta$, let $G(\alpha,\delta)$ denote the class of function $f$, $f(0)=f'(0)-1=0$ for which Re $\{ e^{i\alpha} \frac{2zf'(z)}{f(z)-f(-z)}\}>\delta$. In this paper, we determine the basic properties such as the representation theorem, extreme point and we obtain sharp bound for $a_{n}$ of $G(\alpha,\delta)$.

Received: October 2, 2012

AMS Subject Classification: 30C45

Key Words and Phrases: analytic function, starlike function, representation theorem, extreme points, coefficient bound

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DOI: 10.12732/ijpam.v83i2.8 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 83
Issue: 2