TITLE:
Combinations of Right Half-Plane Mappings and Vertical Strip Mappings Convex in the Vertical Direction
AUTHORS:
Yulin Cai, Zirun She, Fanji Zeng, Lu Huang
KEYWORDS:
Harmonic Mapping, Linear Combination, Cohn’s Rules, Directional Convexi-ty
JOURNAL NAME:
Open Journal of Statistics,
Vol.13 No.6,
December
28,
2023
ABSTRACT: In this
paper, we explore the linear combinations of right half-plane mappings and
vertical strip mappings. We demonstrate that the combinations of these harmonic mappings are convex in the vertical
direction provided they are locally univalent and sense-preserving.
Furthermore, we extend this analysis to a more general case by setting specific
conditions. Additionally, we take some common parameters such as as the dilatation of these harmonic
mappings, and prove the sufficient conditions that their combinations are
locally univalent and convex in the vertical direction. Several examples are constructed by the Mathematica software to demonstrate our main results.