Convex functions of bounded type

Abstract

We introduce a new class of normalized functions univalent and convex in the unit disk. These are called convex of bounded type and the set is denoted by C V ( R 1 , R 2 ) CV({R_1},{R_2}) . For this set we find the Koebe domain, a coefficient bound, and a bound for | f ( z ) | \left | {f(z)} \right | . We also mention a few of the many questions that can be asked about this new class of univalent functions.