JEDNOSTKA NAUKOWA KATEGORII A+

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

## On certain subclasses of multivalently meromorphic close-to-convex maps

### Tom 69 / 1998

Annales Polonici Mathematici 69 (1998), 251-263 DOI: 10.4064/ap-69-3-251-263

#### Streszczenie

Let Mₚ denote the class of functions f of the form $f(z) = 1/z^p + ∑_{k=0}^∞ aₖz^k$, p a positive integer, in the unit disk E = {|z| < 1}, f being regular in 0 < |z| < 1. Let $L_{n,p}(α) = {f: f ∈ Mₚ, Re{-(z^{p+1}/p) (Dⁿf)'} > α}$, α < 1, where $Dⁿf = (z^{n+p} f(z))^{(n)}/(z^p n!)$. Results on $L_{n,p}(α)$ are derived by proving more general results on differential subordination. These results reduce, by putting p =1, to the recent results of Al-Amiri and Mocanu.