关于拟-半-E-凸函数的几个新结论  

Some New Conclusions of Quasi-Semi-E-Convex Function

作　　者：景书杰[1] 王世磊[1] 

机构地区：[1]河南理工大学数学与信息科学学院,河南焦作454000

出　　处：《河南教育学院学报（自然科学版）》2015年第2期9-12,共4页Journal of Henan Institute of Education(Natural Science Edition)

基　　金：河南省一级重点学科支持项目;河南理工大学校级重点学科支持项目

摘　　要：广义E-凸函数作为凸函数的推广在优化理论研究中有着重要的应用.通过对拟-半-E-凸函数已有的性质和结论进行比较与研究,首先给出了拟-半-E-凸函数的有关新性质,并给予了相应的证明;其次分别研究了拟-半-E-凸函数与拟-E-凸函数和半-E-凸函数之间的关系,得出了相关结论;最后给出了关于拟-半-E-凸函数的一个判定定理及其在下半连续情形下的一个判别准则.Generalized E-convex functions are the extension of convex function and have important applications in the study of optimization theory .Firstly, by researching the known properties of quasi-semi-E-convex function, some relative new properties of quasi-semi-E-convex functions were gained and proved .Secondly , the relationship between quasi-semi-E-convex function with quasi-E-convex function and semi-E-convex function were studied , some conclusions were obtained as well .Finally, a judging theorem of quasi-semi-E-convex function and a criteri-on of quasi-semi-E-convex function in the case of lower-semi-continuous were given .

关 键 词：E-凸集 拟-E-凸函数 半-E-凸函数 拟-半-E-凸函数 下半连续函数 

分 类 号：O174.13[理学—数学]