Majorization results for certain subfamilies of analytic functions (Q2025741)

Summary: 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 \(h_1(z)=\sqrt{1+z}\) and \(h_2(z)=1+\sin z\).