Majorization Results for Certain Subfamilies of Analytic Functions

摘要

Let h1ezT and h2ezT be two nonvanishing holomorphic functions in the open unit disc with h1e0T = h2e0T = 1. For some holomorphic function qezT, we consider the class consisting of normalized holomorphic functions f whose ratios fezT/zqezT and qezT are subordinate to h1ezT and h2ezT, respectively. The majorization results are obtained for this class when h1ezT is chosen either h1ezT = cos z or h1ezT = 1 + sin z or h1ezT = ffiffiffiffiffiffiffiffiffi 1 + z p and h2ezT = 1 + sin z.