Univalent harmonic mappings convex in one direction

Abstract In this paper, we present a criterion for a harmonic function to be convex in one direction. Also, we discuss the class of harmonic functions starlike in one direction in the unit disk %${\mathbb D}%$ and obtain a method to construct univalent harmonic functions convex in one direction. Alt...
Ausführliche Beschreibung

Abstract In this paper, we present a criterion for a harmonic function to be convex in one direction. Also, we discuss the class of harmonic functions starlike in one direction in the unit disk %${\mathbb D}%$ and obtain a method to construct univalent harmonic functions convex in one direction. Although the converse of classical Alexander’s theorem for harmonic functions was proved to be false, we obtain a version of converse of it under a suitable additional condition. Ausführliche Beschreibung