Univalent harmonic mappings
Tom 57 / 1992
Annales Polonici Mathematici 57 (1992), 57-70
DOI: 10.4064/ap-57-1-57-70
Streszczenie
Let a < 0, Ω = ℂ -(-∞, a] and U = {z: |z| < 1}. We consider the class $S_H(U,Ω)$ of functions f which are univalent, harmonic and sense preserving with f(U) = Ω and satisfy f(0) = 0, $f_z(0) > 0$ and $f_{z̅}(0) = 0$. We describe the closure $\overline{S_H(U,Ω)}$ of $S_H(U,Ω)$ and determine the extreme points of $\overline{S_H(U,Ω)}$.
