# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

## Some subclasses of close-to-convex functions

### Tom 58 / 1993

Annales Polonici Mathematici 58 (1993), 53-64 DOI: 10.4064/ap-58-1-53-64

#### Streszczenie

For α ∈ [0,1] and β ∈ (-π/2,π/2) we introduce the classes $C_β(α)$ defined as follows: a function f regular in U = {z: |z| < 1} of the form $f(z) = z + ∑_{n=1}^{∞} a_n z^n$, z ∈ U, belongs to the class $C_β(α)$ if $Re{e^{iβ}(1 - α²z²)f'(z)} < 0$ for z ∈ U. Estimates of the coefficients, distortion theorems and other properties of functions in $C_β(α)$ are examined.