Abstract
In this paper, we study the convex combinations of harmonic mappings obtained by shearing a class of slit conformal mappings. Sufficient conditions for the convex combinations of harmonic mappings of this family to be univalent and convex in the horizontal direction are derived. Several examples of univalent harmonic mappings constructed by using these methods are presented to illustrate potential applications of the main results.
| Original language | English |
|---|---|
| Pages (from-to) | 1495-1510 |
| Number of pages | 16 |
| Journal | Bulletin of the Iranian Mathematical Society |
| Volume | 43 |
| Issue number | 5 |
| State | Published - Oct 2017 |
| Externally published | Yes |
Keywords
- Convex combination
- Harmonic mapping
- Shear construction
- Slit mapping