Combinations of Right Half-Plane Mappings and Vertical Strip Mappings Convex in the Vertical Direction  

作　　者：Yulin Cai Zirun She Fanji Zeng Lu Huang Yulin Cai;Zirun She;Fanji Zeng;Lu Huang(Department of Mathematics, Hanshan Normal University, Chaozhou, China;Department of Architecture, Foshan University, Foshan, China;Department of English, Hanshan Normal University, Chaozhou, China)

机构地区：[1]Department of Mathematics, Hanshan Normal University, Chaozhou, China [2]Department of Architecture, Foshan University, Foshan, China [3]Department of English, Hanshan Normal University, Chaozhou, China

出　　处：《Open Journal of Statistics》2023年第6期941-954,共14页统计学期刊（英文）

摘　　要：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.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.

关 键 词：Harmonic Mapping Linear Combination Cohn’s Rules Directional Convexi-ty 

分 类 号：O17[理学—数学]