Characterizations of D-Properly Semi-Prequasi-Invex Mappings

HUANG Yingquan

doi:10.21656/1000-0887.380269

Volume 39 Issue 3

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 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. doi: 10.21656/1000-0887.380269

Citation:

HUANG Yingquan. Characterizations of D-Properly Semi-Prequasi-Invex Mappings[J]. Applied Mathematics and Mechanics, 2018, 39(3): 364-370. doi: 10.21656/1000-0887.380269

Citation:

HUANG Yingquan. Characterizations of D-Properly Semi-Prequasi-Invex Mappings[J]. Applied Mathematics and Mechanics, 2018, 39(3): 364-370. doi: 10.21656/1000-0887.380269

PDF( 316 KB)

Characterizations of D-Properly Semi-Prequasi-Invex Mappings

doi: 10.21656/1000-0887.380269

HUANG Yingquan

College of Mathematics and Statistics, Chongqing Technology and Business University,Chongqing 400067, P.R.China

Funds: The National Natural Science Foundation of China(11471059；11626048；11701057)

Received Date: 2017-10-11
Rev Recd Date: 2017-11-07
Publish Date: 2018-03-15

Abstract

Abstract

The properties of D-properly semi-prequasi-invex mappings were studied. Firstly, it was verified that the η values satisfying condition E exist massively. Secondly, the level set of theD-properly semi-prequasi-invex mapping was proved to be a semi-invex set, and two equivalent propositions of the D-properly semi-prequasi-invex mapping were given with D-upper semi-continuity, *-upper semi-continuity and intermediate-point D-properly semi-prequasi-invexity. Finally, the equivalent relation between the D-properly semi-strict semi-prequasi-invex mapping and the D-properly strict semi-prequasi-invex mapping was established under the condition of the intermediate-point D-properly strict semi-prequasi-invexity.
- D-properly semi-prequasi-invex mapping,
- semi-invex set,
- condition E

FullText(HTML)

References(14)

References

[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]	YANG Xinmin, LI Duan. On properties of preinvex functions[J]. Journal of Mathematical Analysis and Applications,2001,256(1): 229-241.
[5]	YANG Xinmin, LI Duan. Semistrictly preinvex functions[J]. Journal of Mathematical Analysis and Applications,2001,258(1): 287-308.
[6]	YANG Xiaoqi, CHEN Guangya. A class of nonconvex functions and pre-variational inequalities[J]. Journal of Mathematical Analysis and Applications,1992,169(2): 359-373.
[7]	彭建文. 向量值映射D-η-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 prequasiinvex function[J]. Journal of Systems Science and Mathematical Sciences,2003,23(3): 306-314.(in Chinese))
[8]	彭再云, 王堃颍, 赵勇, 等. 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 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))
[9]	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和性质[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))
[10]	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 characterizations of D-〖KG-*4〗semi-preinvexity[J]. Applied Mathematics and Mechanics,2015,36(3): 325-331.(in Chinese))
[11]	杨新民, 戎卫东. 广义凸性及其应用[M]. 北京: 科学出版社, 2016.(YANG Xinmin, RONG Weidong. Generalized Convexity and Its Applications [M]. Beijing: Science Press, 2016.(in Chinese))
[12]	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 applications in optimization problems[D]. PhD Thesis. Hohhot: Inner Mongolia University, 2005.(in Chinese))
[13]	彭再云, 李科科, 张石生.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))
[14]	ity of fractional order Hopfield neural networks[J]. Nonlinear Analysis: Hybrid Systems,2015,16(2): 104-121.