Majorization Results for Certain Subfamilies of Analytic Functions

Abstract

Let h1z and h2z be two nonvanishing holomorphic functions in the open unit disc with h10=h20=1. For some holomorphic function qz, we consider the class consisting of normalized holomorphic functions f whose ratios fz/zqz and qz are subordinate to h1z and h2z, respectively. The majorization results are obtained for this class when h1z is chosen either h1z=cosz or h1z=1+sinz or h1z=1+z and h2z=1+sinz.