%0 Journal Article
%T Integral operators and univalent functions
%A Kiah Wah Ong
%A Sin Leng Tan
%A Yong Eng Tu
%J Tamkang Journal of Mathematics
%D 2012
%I Tamkang University
%R 10.5556/j.tkjm.43.2012.215-221
%X In this paper, we define two new integral operators $L^k$ and $L_k$ which are iterative in nature. We show that for $f(z)=z+a_2z^2+ cdots +a_nz^n +cdots$ with radius of convergence larger than one, $L^kf(z)$ and $L_kf(z)$ when restricted on $E={z:|z|<1}$ will eventually be univalent for large enough $k$. We then show that these are the best possible results by demonstrating that there exists a holomorphic function $T(z)$ in normalized form and with radius of convergence equal to one such that $L^kT(z)$ and $L_kT(z)$ fail to be univalent when restricted to $E$ for every $kin mathbb{N}$.
%K univalent functions
%K integral operator
%U http://journals.math.tku.edu.tw/index.php/TKJM/article/view/630