E-广义单调性及其在广义变分不等式中的应用  

Generalized E-monotonicity and Application to the Generalized Variational Inequality

作　　者：陈乔[1] 罗杰 

机构地区：[1]重庆师范大学生命科学学院,重庆401331 [2]z四川大竹中学,四川大竹635100

出　　处：《重庆师范大学学报（自然科学版）》2014年第5期31-34,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金项目(No.11201240)

摘　　要：引入了一类新的广义单调性即E-伪单调性和E-拟单调性。通过举例说明了E-伪单调性和E-拟单调性的存在性且区别于伪单调性、拟单调性、E-单调性等其他广义单调性。然后主要研究了E-伪单调映射、E-拟单调映射分别与E-伪凸函数、E-拟凸函数间的等价关系。在此基础上提出了E-变分不等式问题,并讨论了E-伪单调性在其中的重要应用。A new kind of generalized monotone mappings called E-pseudomonotone and an E-quasimonotone operator are first intro- duced. In this paper, examples are given to show that the existence of E-pseudomonotone and an E-quasimonotone operator, and the difference with pseudomonotone operator, quasimonotone operator, E-monotone operator. The relationships between E-pseudom- onotone mapping and E-pseudoconvexity are presented, and the relationships between E-quasimonotone mapping and E-quasiconvex- ity are discussed. After this, we give the E-variational inequality problem and study the application of E-pseudoconvexity to it.

关 键 词：E-凸函数 E-伪单调映射 E-拟单调映射 E-变分不等式 

分 类 号：O221.1[理学—运筹学与控制论]