D-η-E-半预不变凸映射和D-η-E-半预不变真拟凸映射

王海英; 符祖峰

doi:10.21656/1000-0887.390143

D-η-E-半预不变凸映射和D-η-E-半预不变真拟凸映射

doi: 10.21656/1000-0887.390143

安顺学院数理学院, 贵州安顺 561000

基金项目: 国家自然科学基金(61304146);贵州省科技厅、安顺市人民政府、安顺学院三方联合科技基金(LH[2017]7052)

详细信息

作者简介:
王海英（1982—），女，教授，硕士（通讯作者. Email: why8206@163.com）.

中图分类号: O211.6
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- 文章访问数: 1152
- HTML全文浏览量: 176
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- 被引次数: 0
出版历程
- 收稿日期: 2018-05-10
- 修回日期: 2018-06-15
- 刊出日期: 2019-03-01

D-η-E-Semi-Preinvex Mapping and D-η-E-Properly Semi-Prequasi-Invex Mapping

School of Mathematics and Physics, Anshun University, Anshun, Guizhou 561000, P.R.China

Funds: The National Natural Science Foundation of China(61304146)

摘要

摘要: 研究了D-η-E-半预不变凸映射和D-η-E-半预不变真拟凸映射的一些性质.首先，讨论了D-η-E-半预不变凸与D-η-E-严格半预不变真拟凸、D-η-E-半严格半预不变真拟凸和D-η-E-半预不变真拟凸之间的关系,在中间点的D-η-E-半预不变凸性和其他一些条件下，得到了它的3个重要的性质定理；其次，对D-η-E-半预不变真拟凸与D-η-E-半严格半预不变真拟凸和D-η-E-严格半预不变真拟凸之间的关系也进行了讨论；最后，获得了D-η-E-半预不变真拟凸映射在优化中的一个重要应用.
- D-η-E-半预不变凸 /
- D-η-E-半预不变真拟凸 /
- D-η-E-半严格半预不变真拟凸 /
- 优化
Abstract: Some properties of the D-η-E-semi-preinvex mapping and the D-η-E-properly semi-prequasi-invex mapping were studied. Firstly, relationships among the D-η-E-semi-preinvex mapping, the semistrictly semi-preinvex mapping, the strictly D-η-E-semi-preinvex mapping and the D-η-E-properly semi-prequasi-invex mapping were discussed. Three important theorems of properties were obtained based on the middle point D-η-E-semi-preinvex and some suitable conditions. Secondly, relationships among the D-η-E-properly semi-prequasi-invex mapping, the semistrictly D-η-E-properly semi-prequasi-invex mapping and the strictly D-η-E-properly semi-prequasi-invex mapping also were addressed. Finally, an important application in terms of the D-η-E-properly semi-prequasi-invex mapping was demonstrated in optimization.
- D-η-E-semi-preinvex /
- D-η-E-properly semi-prequasi-invex /
- semistrictly D-η-E-properly semi-prequasi-invex /
- optimization

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参考文献(15)

[1]	KAZMI K R. Some remarks on vector optimization problems[J]. Journal of Optimization Theory & Applications,1998,96(1): 133-138.
[2]	PENG J W, ZHU D L. On D-preinvex type functions[J]. Journal of Inequalities and Applications,2006,2006: 1-14.
[3]	LONG X J, PENG Z Y, ZENG B. Remark on cone semistrictly preinvex functions[J]. Optimization Letters,2009,3(3): 337-345.
[4]	彭再云, 李科科, 唐平, 等. 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 Zaiyun, LI Keke, TANG Ping, et al. Characterizations and criterions of D -semiprequasi-invex mappings[J]. Journal of Chongqing Normal University(Natural Science),2014,31(5): 18-25.(in Chinese))
[5]	黄应全. 关于向量值 D -半预不变真拟凸映射的刻画[J]. 应用数学和力学, 2018,39(3): 364-370.(HUANG Yingquan. Characterizations of D -properly semi-prequasi-invex mappings[J]. Applied Mathematics and Mechanics,2018,39(3): 364-370.(in Chinese))
[6]	唐莉萍, 杨新民. 关于 D -半预不变凸性的某些新性质[J]. 应用数学和力学, 2015,36(3): 325-331.(TANG Liping, YANG Xinmin. A note on some new characteristics of D -semi-preinvexity[J]. Applied Mathematics and Mechanics,2015,36(3): 325-331.(in Chinese))
[7]	彭建文. 向量值映射 D-η- 半预不变真拟凸的性质[J]. 系统科学与数学, 2003,23(3): 306-314.(PENG Jianwen. Properties of D-η- properly prequasi invex function[J]. Journal of Systems Science and Mathematical Sciences,2003,23(3): 306-314.(in Chinese))
[8]	彭建文. 广义凸性及其在最优化问题中的应用[D]. 博士学位论文. 呼和浩特: 内蒙古大学, 2005.(PENG Jianwen. Generalized convexity with application optimization problems[D]. PhD Thesis. Hohhot: Inner Mongolia University, 2005.(in Chinese))
[9]	龙宪军, 毛小红. 关于向量值映射 D-η- 预不变真拟凸的注记[J]. 云南民族大学学报(自然科学版), 2005,14(3): 213-215.( LONG Xianjun, MAO Xiaohong. Note on properties of D-η- properly prequasi-invex function[J]. Journal of Yunnan Nationalities University(Natural Sciences Edition),2005,14(3): 213-215.(in Chinese))
[10]	LUO Hezhi, WU Huixian, ZHU Yihua. New methods for characterizing D-η- properly prequasi-invex functions[J]. Applied Mathematics: A Journal of Chinese Universities,2006,21(1): 107-112.
[11]	朱见广. 几类广义凸向量值映射的性质及其在最优化理论中的应用[D]. 硕士学位论文. 重庆: 重庆师范大学, 2008.(ZHU Jianguang. Properties of several kinds of generalized convexity functions with applications in optimization theory[D]. Master Thesis. Chongqing: Chongqing Normal University, 2008.(in Chinese))
[12]	ZHOU Mi, WANG Yong, LIU Xiaolan, et al. Properties of D-η- properly prequasi-invex functions[J]. Journal of Hainan Normal University(Natural Science),2009,22(4): 365-370, 407.
[13]	LI Taiyong, HUANG Min. On the characterizations of D- preinvex functions[J]. Journal of Inequalities and Applications,2012,〖STHZ〗 2012: 240. DOI: 10.1186/1029-242X-2012-240.
[14]	彭再云, 王堃颍, 赵勇, 等. D-η- 半预不变凸映射的性质及其应用[J]. 应用数学和力学, 2014,35(2): 202-211.(PENG Zaiyun, WANG Kunying, ZHAO Yong, et al. Characterizations and applications of D-η- semipreinvex mappings[J]. Applied Mathematics and Mechanics,2014,35(2): 202-211.(in Chinese))
[15]	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 Zaiyun, LI Keke, ZHANG Shisheng. D-η-E- semipreinvex vector mappings and vector optimization[J]. Applied Mathematics and Mechanics,2014,35(9): 1020-1032.(in Chinese))