Harmonic mappings onto R-convex domains

Abstract

The plane domain D is called R-convex if D contains each compact set bounded by two shortest sub-arcs of the radius R with endpoints w1, w2 ∈ D, |w1−w2| <= 2R. In this paper, we prove the conditions of R-convexity for images of disks under harmonic sense preserving functions. The coefficient bounds for harmonic mappings of the unit disk onto R-convex domains are obtained.

Keywords

• R-convex domains
• coefficient bounds
• harmonic mappings
• coefficient bounds