Some Transformation Properties with Omitted Value

Abstract

The purpose of this paper is to show that for a holomorphic and univalent function in class S, an omitted –value transformation yields a class of starlike functions as a rotation transformation of the Koebe function, allowing both the image and rotation of the function to be connected. Furthermore, these functions have several properties that are not far from a convexity properties. We also show that Pre- Schwarzian derivative is not invariant since the convexity property of the function is so weak.