Γ-convexity  

作　　者：Zhouqin JIA Wenzhi LIU Liping YUAN Tudor ZAMFIRESCU 贾卓琴;刘文治;苑立平;詹姆法尔斯库杜德(School of Mathematical Sciences,Hebei Normal University,Shijiazhuang,050024,China;Hebei Key Laboratory of Computational Mathematics and Applications,Shijiazhuang,050024,China)

机构地区：[1]School of Mathematical Sciences,Hebei Normal University,Shijiazhuang,050024,China [2]Hebei Key Laboratory of Computational Mathematics and Applications,Shijiazhuang,050024,China

出　　处：《Acta Mathematica Scientia》2025年第1期3-15,共13页数学物理学报(B辑英文版)

基　　金：supported by the NSFC(12271139,11871192);the High-end Foreign Experts Recruitment Program of People’s Republic of China(G2023003003L);the Program for Foreign experts of Hebei Province;the Natural Science Foundation of Hebei Province(A2023205045);the Special Project on Science and Technology Research and Development Platforms,Hebei Province(22567610H);the program for 100 Foreign Experts Plan of Hebei Province.

摘　　要：Let F be a family of sets in R^(d)(always d≥2).A set M■R^(d)is called F-convex,if for any pair of distinct points a,y∈M,there is a set F∈F such that x,y∈F and F■M.We obtain theΓ-convexity,when F consists of F-paths.AΓ-path is the union of both shorter sides of an isosceles right triangle.In this paper we first characterize some I-convex sets,bounded or unbounded,including triangles,regular polygons,subsets of balls,right cylinders and cones,unbounded planar closed convex sets,etc.Then,we investigate the F-starshaped sets,and provide some conditions for a fan,a spherical sector and a right cylinder to be F-starshaped.Finally,we study theΓ-triple-convexity,which is a discrete generalization ofΓ-convexity,and provide characterizations for all the 4-point sets,some 5-point sets and Z^(d)to beΓ-triple-convex.

关 键 词：Γ-convexity Γ-starshaped sets Γ-triple-convexity 

分 类 号：O17[理学—数学]