Abstract
Let h(1)(z) and h(2)(z) be two nonvanishing holomorphic functions in the open unit disc with h(1)(0) = h(2)(0) = 1. For some holomorphic function q(z), we consider the class consisting of normalized holomorphic functions f whose ratios f(z)/zq(z) and q(z) are subordinate to h(1)(z) and h(2)(z), respectively. The majorization results are obtained for this class when h(1)(z) is chosen either h(1)(z) = cos z or h(1)(z) = 1 + sin z or h(1)(z) = root 1 + z and h(2)(z) = 1 + sin z.