半严格F-G广义凸函数  

Semi-strictly F-G Generalized Convex Functions

作　　者：赵宇[1] 黄金莹[1] 

机构地区：[1]佳木斯大学理学院数学系,黑龙江佳木斯154007

出　　处：《重庆师范大学学报（自然科学版）》2011年第1期7-12,共6页Journal of Chongqing Normal University:Natural Science

基　　金：黑龙江省教育厅科技研究项目(No.11551499)

摘　　要：定义了广义凸集和F-G广义凸函数等概念,进而给出半严格F-G广义凸函数概念,并将已有文献中提出的条件C推广为条件P1、P2,指出条件P1、P2的若干性质,得到其所蕴含的等式关系: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]。并在此基础上给出半严格F-G广义凸函数的两个充分条件,指出在一定条件下,满足中间点半严格F-G广义凸性的F-G广义凸函数是半严格F-G广义凸函数。最后列举了若干满足本文结论的向量值函数F和数量函数G的具体形式,并给出半严格F-G广义凸函数在极小化问题中的应用。This paper defines generalized convex sets and generalized convex functions,furthermore gives the definition of Semi-strictly F-G generalized convex functions.It generalizes the conditions C of reference[5] to conditions P1,P2,gives their properities and obtains the equal relation between conditions P1 and P2.The relation is supposed F to satisfy conditions P1 and P2 over K,then for any λ∈（0,1）and for any u1,u2∈,u1≠u2,then for all x,y∈K,we have F（x,y,λu1＋（1-λ）u2）=F[F（x,y,u1）,F（x,y,u2）,λ].Based on this,comparing to reference[9] and ,the author gives two sufficient conditions of semi-strictly F-G generalized convex functions and gives that under certain conditions,F-G generalized convex functions is semi-strictly F-G generalized convex functions when F-G generalized convex functions satisfy intermediate-point semi-strictly F-G generalized convexity.At last,this paper enumerates several vector valued functions F and numerical functions G and the applications of semi-strictly F-G generalized convex functions in minimization problems.

关 键 词：半严格F-G广义凸函数 广义凸集 F-G广义凸函数 条件P1 条件P2 

分 类 号：O174.13[理学—数学]