Clunie, J. and Sheil-Small, T. (1984) Harmonic Univalent Functions. Annales Academiae Scientiarum Fennicae, 9, 3-25.
https://doi.org/10.5186/aasfm.1984.0905

has been cited by the following article:

• 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.