Majorization and pseudo-subordination of a class of analytic functions

Abstract

In this thesis, we combine techniques used in Barnard and Kellogg's paper, Ruscheweyh's subordination result, (1.4), variational techniques, and geometric properties of Mobius transformations to verify the following theorem: Theorem 1.1. If F G K* and f ^w F in D with /'(0) > 0, then f < F' for z G F>i and the result is sharp.