广义凸函数与弱近似凸集  

Generalized convex functions and weak nearly convex sets

作　　者：黄金莹[1] 赵宇[1] 

机构地区：[1]佳木斯大学理学院,佳木斯154007

出　　处：《黑龙江大学自然科学学报》2011年第2期200-205,209,共7页Journal of Natural Science of Heilongjiang University

基　　金：黑龙江省教育厅科学技术研究资助项目(11551499)

摘　　要：定义广义凸集和F-G广义凸函数等概念,并给出条件P1、P2,指出:若F在K上满足条件P1、P2,则λ∈(0,1),u1,u2∈[0,1],u1≠u2,x,y∈K,有F(x,y,λu1+(1-λ)u2)=F[F(x,y,u1),F(x,y,u2),λ]。P1采用集合方法研究F-G广义凸函数。首先给出闭弱近似凸集是凸集的一个新证明,其次构造集合Afx,y,并利用条件P1、P2,得到集合Afx,y具有弱近似凸性的两个充分条件;最后作为应用得到与下半连续性相关的F-G广义凸函数的充分条件和若干推论。The definitions of generalized convex sets,F-G generalized convex functions,and conditions P1 and P2 are given.Furthermore,it is pointed out that if F satisfies conditions P1 and P2 over K,then F（x,y,λu1＋（1-λ）u2）=F[F（x,y,u1）,F（x,y,u2）,λ] for any λ∈（0,1）,u1,u2∈,u1≠u2 and x,y∈K.The method of sets is used to study the F-G generalized convex functions.Firstly,a new proof of closed weak nearly convex sets is convex sets is given.Secondly,constructs sets Afx,y and obtains two sufficient conditions of sets Afx,y have weak nearly convexity by using conditions P1 and P2.At last,as applications,the sufficient conditions and some corollaries of F-G generalized convex functions which is related with lower semi-continuity are obtained.

关 键 词：F-G广义凸函数 弱近似凸集 条件P1 条件P2 

分 类 号：O174.13[理学—数学]