严格拟凸函数的几个判别准则  

Several Criteria for Strictly Quasi-Convex Functions

作　　者：杨丹 YANG Dan(College of Mathematics and Statistics,Kashi University,Kashi 844008,Xinjiang,China)

机构地区：[1]喀什大学数学与统计学院,新疆喀什844008

出　　处：《咸阳师范学院学报》2021年第4期11-13,共3页Journal of Xianyang Normal University

基　　金：新疆维吾尔自治区自然科学基金项目(2020D01B04);喀什大学科研基金项目(20202698)。

摘　　要：研究在较弱条件下严格拟凸函数的判别准则。举例论证文中研究条件比常用条件更弱;证明在文中条件下,如果f是下半连续或拟凸函数或凸函数或半严格拟凸函数,则f为严格拟凸函数;应用反例说明在上半连续条件下是不成立的。A study was made of the criteria of strictly quasiconvex functions under weaker conditions.Examples have been given to demonstrate that the research conditions in this paper are weaker than the common conditions.It is proved that if it is a lower semicontinuous or quasiconvex function or a convex or semi strictly quasiconvex function,then it is a strictly quasiconvex function.It is further proved that if it is a lower semicontinuous or quasiconvex function or a convex or semi strictly quasiconvex function,then it is a strictly quasiconvex function.A counter example has been given to show that it does not hold under the condition of upper semicontinuity.

关 键 词：拓扑线性空间 严格拟凸函数 判别准则 

分 类 号：O174.13[理学—数学]