Classes of univalent functions with weight. (Q1432251)

The author [Dokl. Akad. Nauk 349, No. 6, 727--728 (1996; Zbl 0894.30016)] introduced the class \(Q=\{f(z): zf(z)\in S\}\) of univalent functions with weight \(z\). By the same token, four classes are defined here as counterparts of well-known subclasses of close-to-convex, close-to-starlike functions, functions of bounded rotation, and functions \(F\in S\) satisfying the condition \(|F'(z)-1|<1\), \(|z|<1.\) Several theorems are announced which establish various relations between these and previously introduced classes as well as sharp estimates for the coefficients and distortion-like theorems.