Majorization Results for Certain Subfamilies of Analytic Functions

[摘要] Let h1ðzÞ and h2ðzÞ be two nonvanishing holomorphic functions in the open unit disc with h1ð0Þ = h2ð0Þ = 1. For some holomorphic function qðzÞ, we consider the class consisting of normalized holomorphic functions f whose ratios fðzÞ/zqðzÞ and qðzÞ are subordinate to h1ðzÞ and h2ðzÞ, respectively. The majorization results are obtained for this class when h1ðzÞ is chosen either h1ðzÞ = cos z or h1ðzÞ = 1 + sin z or h1ðzÞ = ffiffiffiffiffiffiffiffiffi 1 + z p and h2ðzÞ = 1 + sin z.

[学科分类] 护理学