河南教育学院学报（自然科学版）
河南教育學院學報（自然科學版）
하남교육학원학보（자연과학판）
JOURNAL OF HENAN EDUCATION INSTITUTE (NATURAL SCIENCE EDITION)
2015年
2期
9-12
,共4页
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
E-凸集%擬-E-凸函數%半-E-凸函數%擬-半-E-凸函數%下半連續函數
E-철집%의-E-철함수%반-E-철함수%의-반-E-철함수%하반련속함수
E-convex sets%quasi-E-convex function%semi-E-convex function%quasi-semi-E-convex function%low-er-semi-continuous function
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。
廣義E－凸函數作為凸函數的推廣在優化理論研究中有著重要的應用。通過對擬－半－E－凸函數已有的性質和結論進行比較與研究，首先給齣瞭擬－半－E－凸函數的有關新性質，併給予瞭相應的證明；其次分彆研究瞭擬－半－E－凸函數與擬－E－凸函數和半－E－凸函數之間的關繫，得齣瞭相關結論；最後給齣瞭關于擬－半－E－凸函數的一箇判定定理及其在下半連續情形下的一箇判彆準則。
엄의E－철함수작위철함수적추엄재우화이론연구중유착중요적응용。통과대의－반－E－철함수이유적성질화결론진행비교여연구，수선급출료의－반－E－철함수적유관신성질，병급여료상응적증명；기차분별연구료의－반－E－철함수여의－E－철함수화반－E－철함수지간적관계，득출료상관결론；최후급출료관우의－반－E－철함수적일개판정정리급기재하반련속정형하적일개판별준칙。
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 .
