球面凸分析进展Ⅰ  

Review on spherically convex analysis I

作　　者：国起 GUO Qi(School of Mathematical Sciences,SUST,Suzhou 215009,China)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009

出　　处：《苏州科技大学学报（自然科学版）》2023年第3期1-10,35,共11页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金资助项目(12071334,11671293)。

摘　　要：作为球面凸分析研究进展综述的第一部分,在对球面凸性理论中各研究方向的发展过程与现状予以非常简要的分析后,论文重点汇集并讨论与球面凸集有关的基本概念和结论,包括欧氏单位球面上的二元运算和典型变换、球凸集的组合性质与结构性质等,同时提出了一些待解决的基础性问题。This is the first part of a brief survey of recent progress in spherically convex analysis.A very brief introduction is given on the history and developments in various aspects of the spherical convexity.Then it focuses on the basic definitions and properties of spherically convex sets including the binary operations and the classical transformations,the combinatorial and structural properties on the Euclidean unit sphere Sr-1.Several basic questions are also proposed.

关 键 词：球面凸性 球面二元运算 组合性质 结构性质 

分 类 号：O18[理学—数学]