<em>D-η</em>-半预不变凸映射的性质与应用

彭再云; 王堃颍; 赵勇; 张石生

doi:10.3879/j.issn.1000-0887.2014.02.008

D-η-半预不变凸映射的性质与应用

doi: 10.3879/j.issn.1000-0887.2014.02.008

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

基金项目: 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)

详细信息

作者简介:
彭再云(1980—)，男，重庆人，副教授，博士(E-mail: pengzaiyun@126.com)

中图分类号: O221.1
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出版历程
- 收稿日期: 2013-07-16
- 刊出日期: 2014-02-15

Characterizations and Applications of D-η-Semipreinvex Mappings

¹School of Science, Chongqing Jiaotong University, Chongqing 400074, P.R.China;²School of Mathematics Science, Chongqing Normal University, Chongqing 401331, P.R.China;³Department of Statistics and Mathematics,Yunnan University of Finance and Economics, Kunmin 650224, P.R.China

Funds: The National Natural Science Foundation of China(11271389; 11301571)

摘要

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.
- D-&eta /
- -半预不变凸映射 /
- 判定定理 /
- 优化问题 /
- 应用
Abstract: A class of new vector valued generalized convex mappings—D-η-semipreinvex mappings, which was a true generalization of D-preinvex mapping, was given. Firstly, examples were given to show the existence of D-η-semipreinvexmappings and illustrate the differences between D-η-semistrictly semi-preinvex and D-η-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.
- D-&eta /
- -semipreinvex mappings /
- criterion /
- vector optimization /
- applications

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参考文献(13)

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