Journal of Function Spaces (Jan 2021)
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.