D-半预不变凸映射的一些判别准则  

Some Criteria for D-Semi-Preinvex Mappings

作　　者：杨玉红[1,2] YANG Yuhong(School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021;School of Mathematics and Statistics, Yangtze Normal University, Fuling Chongqing 408100, China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]长江师范学院数学与统计学院,重庆涪陵408100

出　　处：《重庆师范大学学报（自然科学版）》2018年第3期21-29,共9页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11431004);重庆市教委项目(No.KJ160013)

摘　　要：【目的】为锥意义下的半预不变凸映射提供一些判别准则。【方法】利用向量值映射的半连续性、中间点凸性等条件。【结果】首先,在向量值映射的半连续性条件下,可以用中间点的D-半预不变凸性来刻画D-半预不变凸性;其次,在D-半严格半预不变凸性条件下,通过中间点的D-半预不变凸性获得了D-半预不变凸性;最后,在D-半严格半预不变凸性和下半连续条件下给出了D-半预不变凸性的充分条件。【结论】所得的结果将相关文献的一些结论推广到了向量值半预不变凸情形。[Purposes]The purpose is to provide some criteria for semi-preinvex mappings in the sense of cones. [Methods]It makes use of vector-valued mappings＇ semi-continuity,intermediate-point convexity,etc. [Findings] Firstly,under the condition of vector-valued mappings＇ semi-continuity,D-semi-preinvexity is characterized by intermediate-point D-semi-preinvexity. Secondly,if D-semistrict semi-preinvexity holds,then D-semi-preinvexity can be obtained through intermediate-point D-semi-preinvexity. And lastly,sufficient conditions for Dsemi-preinvexity are established based on D-semistrict semi-preinvexity and lower semi-continuity. [Conclusions]The obtained results generalize some conclusions in related literatures to vector-valued semi-preinvex case.

关 键 词：半不变凸集 D-半预不变凸 D-半严格半预不变凸 条件E 

分 类 号：O221.6[理学—运筹学与控制论]