General Mathematics, Vol. 7, pp. 25-38, 1999
Abstract:
Let $\, \Sigma(p) \, $ denote the class of functions
of the form
$$
f(z) = \frac{a_{p-1}}{z^p}+\sum_{n=1}^\infty
a_{p+n-1}z^{p+n-1}, \; \;
a_{p-1}>0, \; \; a_{p+n-1}\ge 0, \; \; p \in \mathbb{N} = \{1, 2, ... \},
$$
which are regular and p-valent in the punctured disc $\, U^* = \{z\, : \,
0<|z|<1 \}. \,$ Let $ \, \Sigma_i(p) \,$ ($i \in \{0,1\}$) denote the subclasses
of $\, \Sigma (p) \, $ satisfying $\, z_0^p f(z_0) =1 \, $ and $\, -z_0^{p+1}f'(z_0)
=p, \,$ respectively. In this paper we obtain coefficient estimates,
a distortion theorem, closure theorems and a radius of convexity of order
$\, \delta \; \; (0\le\delta Full text of the article: