强拟\alpha-预不变凸函数

运筹学学报 ›› 2015, Vol. 19 ›› Issue (1): 77-84.

强拟\alpha-预不变凸函数

王海英¹, 符祖峰^1,*

1. 安顺学院数理学院, 贵州安顺 561000

收稿日期:2013-12-11 出版日期:2015-03-15 发布日期:2015-03-15
通讯作者: 符祖峰 E-mail:why8206@163.com
基金资助:
国家自然科学青年基金(No. 61304146)，贵州省高校优秀科技创新人才支持计划资助项目(黔教合KY字[2012]101号)，贵州省科技厅、安顺市人民政府、安顺学院三方联合基金(黔科合J字LKA[2013]19号)

The strongly quasi \alpha-preinvex functions

WANG Haiying¹, FU Zufeng^1,*

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

Received:2013-12-11 Online:2015-03-15 Published:2015-03-15

摘要/Abstract

摘要： 研究了一类重要的广凸函数------强拟$\alpha$-预不变凸函数，讨论了它与拟\,$\alpha$-预不变凸函数、严格拟\,$\alpha$-预不变凸函数及半严格拟\,$\alpha$-预不变凸函数之间的关系，并在中间点的强拟\,$\alpha$-预不变凸性下得到了它的三个重要的性质定理，同时给出了强拟\,$\alpha$-预不变凸函数在数学规划中的两个重要应用，这些结果在一定程度上完善了对强拟\,$\alpha$-预不变凸函数的研究.

关键词: 强拟\alpha-预不变凸函数, 拟\alpha-预不变凸函数, 严格拟\alpha-预不变凸函数, 半严格拟 \alpha-预不变凸函数

Abstract: In this paper, one important type of generalized convex functions termed as strongly quasi $\alpha$-preinvex functions is studied. The relationships among strongly quasi $\alpha$-preinvex functions and quasi $\alpha$-preinvex functions, and strictly quasi $\alpha$-preinvex functions and semistrictly quasi $\alpha$-preinvex functions have been discussed. Three important theorems of properties have been obtained for it on the middle point strongly quasi $\alpha$-preinvexity. We also present two important applications in terms of strongly quasi $\alpha$-preinvex functions in mathematical programming. These results complete the researches for the strongly quasi $\alpha$-preinvex functions to some extent.

Key words: strongly quasi $\alpha$-preinvex functions, quasi $\alpha$-preinvex functions, strictly quasi $\alpha$-preinvex functions, semistrictly quasi $\alpha$-preinvex functions

中图分类号:

O176
O177.9

王海英, 符祖峰. 强拟\alpha-预不变凸函数[J]. 运筹学学报, 2015, 19(1): 77-84.

WANG Haiying, FU Zufeng. The strongly quasi \alpha-preinvex functions[J]. Operations Research Transactions, 2015, 19(1): 77-84.

参考文献

Weir T, Jeyakumar V. A class of nonconvex functions and mathematical programming [J]. Bull Austral Math Soc, 1988, 38: 177-189.

Yang X M, Li D. Semistrictly preinvex functions [J]. Journal of Mathematical Analysis and Applications, 2001, 258: 287-308.

Tang W M, Yang X M. The sufficiency and necessity conditions of strongly preinvex functions [J]. 2006, 3:50-58.

Tang W M, Yang X M. The sufficiency and necessity conditions of strongly preiquasi-Invex functions [J]. 2007, 3: 21-58.
Noor M A, Noor K I. Some characterizations of strongly preinvex functions [J]. Journal of Mathematical Analysis and Applications, 2006, 316: 697-706.

刘彩平. 几类广义不变凸函数及其性质 [D]. 重庆: 重庆师范大学, 2008.
Noor M A, Noor K I. Some characterizations of strongly preinvex functions [J]. Journal of Mathematical Analysis and Applications, 2006, 316: 697-706.

张芳. 半严格拟\alpha-预不变凸函数的一个充分条件 [J]. 长春大学学报, 2008, 1: 7-9.

Noor M A. On Generalized preinvex Functions and monotonicities [J]. Journal of Inequality Pure Applied Mathematics, 2004, 4: 1-9.

Tang W M. On strictly and semistrictly quasi $\alpha$-preinvex functions [J]. Journal of Computational Analysis and Applications, 2013, 8: 1391-1402.

Yang X M, Yang X Q, Teo K L. Characterizations and applications of prequasiinvex functions [J]. Journal of Optimization Theory Applications, 2001, 3: 645-668.

LUO H Z, Xu Z K. On characterizations of prequasi-invex functions [J]. Journal of Optimization Theory Applications, 2004, 2: 429-439.
Noor M A, Noor K I. Some characterizations of strongly preinvex functions [J]. Journal of Mathematical Analysis and Applications, 2006, 316: 697-706.

Noor M A, Noor K I. Some characterizations of strongly preinvex functions [J]. Journal of Mathematical Analysis and Applications, 2006, 316: 697-706.

刘彩平. 半严格不变凸函数 [J]. 运筹学学报, 2007, 4: 85-92.
王海英, 武慧虹. 半连续函数的预不变凸性 [J]. 河南科技大学学报(自然科学版), 2011, 3: 75-78.