文档介绍：第 38 卷第 1 期 苏州科技大学学报（自 然 科 学 版） Ｖｏｌ．38 Ｎｏ．1
２０21 年 3 月 Ｊｏｕｒes were given later （see，. [3－6]）. We would like to point
out that，among all these definitions，the one given in [4] or [6] is of its own feature：it is the only one given in the
analytic form.
The earlier study on spherical convexity focused on combinatorial properties of spherically convex sets （with
different definitions），such as，the theorems of Helly’s type （see，. [2，7-9] and the references therein）. Then，
the studies on other properties and applications of spherical convexity emerged gradually （see 3，10-13]）. Re鄄
cently，the theorems of Radon’s type and Carathéodory’s type were established in [6]. More interestingly，in [14]
the concept of （spherically） convex function defined on the so-called weakly convex sets in a sphere was intro鄄
duced and investigated systematically，. as an application，necessary and suffcient optimality conditions for
constrained convex optimization problems on the sphere are derived. The spherical minimax location problem was
studied in [15-16]. There are too many references to mention here.
Although some progresses have been made in the study on spherical convexity，the task to establish a sys鄄
tematic theory of spherical convexity is far away from being completed，simply because many counterpart