A class of univalent functions. II
For part I see the author in Hokkaido Math. J. 27, No. 2, 329-335 (1998; Zbl 0908.30009). In this paper the author considers the class \({\mathcal F}\) of analytic functions \(f(z)\) in the open unit disc \(U\) of the complex plane with \(f(0)=0=1-f'(0)\) and satisfying \(|f'(z) ({z\over f(z)})^{1+\mu}-1\mid <\lambda(z\in U)\) where \(0<\mu<1\), \(0<\lambda\leq 1\). The author obtains representation theorems, distortion theorems, and identifies some subclasses of \({\mathcal F}\) for which \(\text{Re}(f'(z))>0\) holds for \(z\in U\). The author unfortunately does not mention whether his results are sharp.
scientific article; zbMATH DE number 1396099