IJPAM: Volume 52, No. 4 (2009)

SOME PROPERTIES OF UNIVALENT FUNCTIONS

M. Nunokawa$^1$, S. Owa$^2$, T. Hayami$^3$, K. Kuroki$^4$
$^1$University of Gunnma
798-8, Hoshikuki-machi, Chuo-ku
Chiba-Shi, Chiba, 260-0808, JAPAN
e-mail: mamoru_nuno@doctor.nifty.jp
$^{2,3,4}$Department of Mathematics
Faculty of Science and Technology
Kinki University
Higashi-Osaka, Osaka, 577-8502, JAPAN
$^2$e-mail: owa@math.kindai.ac.jp
$^3$e-mail: ha_ya_to112@hotmail.com
$^4$e-mail: freedom@sakai.zaq.ne.jp


Abstract.For some univalent functions $f(z)$ which are normalized by $f(0)=0$ and $f'(0)=1$ in the open unit disk $\mathbb{U}$, some properties for the length $L(r)$ of the image curve $C(r)$ by $w=f(z)$ of $\vert z\vert=r<1$ are considered. It is the object of the present paper to derive properties for lengths $L(r)$ by close-to-convex functions and Bazilevi ${\rm\check{c}}$ functions.

Received: April 2, 2009

AMS Subject Classification: 30C45

Key Words and Phrases: starlike, convex, close-to-convex, Bazilevi ${\rm\check{c}}$ function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 4