D-η-半预不变凸映射的性质与应用  

Characterizations and Applications of D-η-Semipreinvex Mappings

作　　者：彭再云[1] 王堃颍 赵勇[2] 张石生[3] 

机构地区：[1]重庆交通大学理学院.重庆400074 [2]重庆师范大学数学学院,重庆401331 [3]云南财经大学数学与统计学院,昆明650224

出　　处：《应用数学和力学》2014年第2期202-211,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11271389;11301571);重庆市自然科学基金(CSTC2012jjA00016);重庆市教委基金(KJ130428)~~

摘　　要：提出了一类新的向量值映射——D-η-半预不变凸映射,它是D-预不变凸映射的真推广.首先,用例子说明了D-η-半预不变凸映射的存在性,并说明其区别于D-η-半严格半预不变凸映射;然后,给出了D-η-半预不变凸映射的判定定理,并建立了D-η-半预不变凸映射与D-η-严格/半严格半预不变凸映射间的关系;最后,讨论了D-η-半严格半预不变凸映射在优化问题中的应用,并举例验证了所得结论的正确性.A class of new vector valued generalized convex mappings-- D-η- semipreinvex map- pings, which was a true generalization of D- preinvex mapping, was given. Firstly, examples were given to show the existence of D-v- semipreinvexmappings and illustrate the differences between D-η- semistrictly semi-preinvex and D-v- semipreinv exmapping. Secondly, a criterion of D-η- semipreinv exity was given, and the relationships among D-η- semipreinvexity, D-η- strict semipreinvexity and D-η- semistrict semipreinvexity were discussed. Finally, an important application of D-η- semistrict semipreinvexity in vector optimization was discussed, then give an example was given to illustrate the result.

关 键 词：D-η-半预不变凸映射 判定定理 优化问题 应用 

分 类 号：O174.56[理学—数学]