关于<em>D</em>-半预不变凸性的某些新性质

唐莉萍; 杨新民

doi:10.3879/j.issn.1000-0887.2015.03.010

关于D-半预不变凸性的某些新性质

doi: 10.3879/j.issn.1000-0887.2015.03.010

唐莉萍¹,
杨新民²

¹上海大学数学系, 上海 200444;²重庆师范大学数学科学学院, 重庆 400047

基金项目: 国家自然科学基金(重点项目)（11431004）；国家自然科学基金（11271391）

详细信息

作者简介:
唐莉萍（1985—），女，四川资中人，博士生(E-mail: tanglipings@163.com);杨新民（1960—），男，四川沪州人，教授，博士生导师(通讯作者. E-mail: xmyang@cqnu.edu.cn).

中图分类号: O221.6
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出版历程
- 收稿日期: 2014-12-09
- 修回日期: 2014-12-24
- 刊出日期: 2015-03-15

A Note on Some New Characteristics of D-Semi-Preinvexity

TANG Li-ping¹,
YANG Xin-min²

¹Institute of Tribology, Hefei University of Technology, Hefei 230009, P.R.China;²College of Chemistry and Chemical Engineering, Beifang University of Nationalities, Yinchuan 750021, P.R.China

Funds: The National Natural Science Foundation of China（Key Program）（11431004）;The National Natural Science Foundation of China(11271391)

摘要

摘要: 研究了锥意义下的半预不变凸性的新性质.首先，对彭再云等的文献(彭再云, 李科科, 唐平, 黄应全.向量值D-半预不变真拟凸映射的判定与性质[J].重庆师范大学学报(自然科学版), 2014,31( 5 ): 18-25.)中的例4进行了修正，使其满足条件E.然后，给出了条件E₁的一个重要性质，并在此基础上结合稠密性结果，分别利用D-半严格半预不变真拟凸性和D-严格半预不变真拟凸性建立了D-半预不变凸性的刻画.最后利用D-半预不变真拟凸性给出了D-预不变凸性的刻画.
- D-半预不变凸 /
- D-半严格半预不变真拟凸 /
- D-严格半预不变真拟凸 /
- D-半预不变真拟凸
Abstract: Some new properties of semi-preinvexity in the sense of cones were studied. Firstly, Example 4 in the paper of PENG Zai-yun, etc.(PENG Zai-yun, LI Ke-ke, TANG Ping, HUANG Ying-quan. Characterizations and criterions of D-semiprequasi-invex mappings[J].Journal of Chongqing Normal University(Natural Science),2014,31( 5 ):18-25.) was modified to satisfy condition E. Then, an important property of condition E₁ was obtained. Based on this property and the results of density, two characterizations of D-semi-preinvexity were established by means of D-semi-strict semi-prequasiinvexity and D-strict semi-prequasiinvexity, respectivley. In the end,D-semi-preinvexity was characterized with D-semi-prequasiinvexity.
- D-semi-preinvexity /
- D-semi-strict semi-prequasiinvexity /
- D-strict semi-prequasiinvexity /
- D-semi-prequasiinvexity

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参考文献(12)

[1]	Hanson M A. On sufficiency of the Kuhn-Tucker conditions[J].Journal of Mathematical Analysis and Applications,1981,80(2): 545-550.
[2]	Weir T, Mond B. Pre-invex functions in multiple objective optimization[J].Journal of Mathematical Analysis and Applications,1988,136(1): 29-38.
[3]	Weir T, Jeyakumar V. A class of nonconvex functions and mathematical programming[J].Bulletin of the Australian Mathematical Society,1988,38(2): 177-189.
[4]	Mohan S R, Neogy S K. On invex sets and preinvex functions[J].Journal of Mathematical Analysis and Applications,1995,189(3): 901-908.
[5]	Yang X M, Li D. On properties of preinvex functions[J].Journal of Mathematical Analysis and Applications,2001,256(1): 229-241.
[6]	Yang X M, Li D. Semistrictly preinvex functions[J].Journal of Mathematical Analysis and Applications,2001,258(1): 287-308.
[7]	Yang J, Yang X. Two new characterizations of preinvex functions[J].Dynamics of Continuous, Discrete & Impulsive Systems B,2012,19(3): 405-410.
[8]	Yang X. A note on preinvexity[J].Journal of Industrial and Management Optimization,2014,10(4): 1319-1321.
[9]	Yang X Q, Chen G Y. A class of nonconvex functions and pre-variational inequalities[J].Journal of Mathematical Analysis and Applications,1992,169(2): 359-373.
[10]	彭再云, 王堃颍, 赵勇, 张石生. D-η-半预不变凸映射的性质与应用[J]. 应用数学和力学, 2014,35(2): 202-211.(PENG Zai-yun, WANG Kun-ying, ZHAO Yong, ZHANG Shi-sheng. Characterizations and applications of D-η-semipreinvex mappings[J].Applied Mathematics and Mechanics,2014,35(2): 202-211.(in Chinese))
[11]	彭再云, 李科科, 唐平, 黄应全. 向量值D-半预不变真拟凸映射的判定与性质[J]. 重庆师范大学学报(自然科学版), 2014,31(5): 18-25.(PENG Zai-yun, LI Ke-ke, TANG Ping, HUANG Ying-quan. Characterizations and criterions of D-semiprequasi-invex mappings[J].Journal of Chongqing Normal University(Natural Science),2014,31(5): 18-25.(in Chinese))
[12]	彭再云, 李科科, 张石生. 向量D-η-E-半预不变凸映射与向量优化[J]. 应用数学和力学, 2014,35(9): 1020-1032.(PENG Zai-yun, LI Ke-ke, ZHANG Shi-sheng. D-η-E-Semipreinvex vector mappings and vector optimization[J].Applied Mathematics and Mechanics, 2014,35(9): 1020-1032. (in Chinese))