大学数学
大學數學
대학수학
COLLEGE MATHEMATICS
2011年
6期
105-110
,共6页
广义凸集%广义凸函数%中间点广义凸函数%端点广义凸函数%条件P1%稠密性定理
廣義凸集%廣義凸函數%中間點廣義凸函數%耑點廣義凸函數%條件P1%稠密性定理
엄의철집%엄의철함수%중간점엄의철함수%단점엄의철함수%조건P1%주밀성정리
generalized convex sets%generalized convex functions%intermediate-point generalized convex functions%endpoint generalized convex functions%condition P1%density theorem
提出广义凸集、广义凸函数、中间点广义凸函数、端点广义凸函数四个定义，通过定义条件P1，研究条件P1所蕴含的等式关系，进而得到一个基础性定理一稠密性定理和一个相对条件较弱的推论，最后将结果应用于若干不同类型的广义凸函数类，尤其是s-凸函数、几何凸函数、rp-凸函数，得到它们所共有的一个特征性质，即满足稠密性定理．
提齣廣義凸集、廣義凸函數、中間點廣義凸函數、耑點廣義凸函數四箇定義，通過定義條件P1，研究條件P1所蘊含的等式關繫，進而得到一箇基礎性定理一稠密性定理和一箇相對條件較弱的推論，最後將結果應用于若榦不同類型的廣義凸函數類，尤其是s-凸函數、幾何凸函數、rp-凸函數，得到它們所共有的一箇特徵性質，即滿足稠密性定理．
제출엄의철집、엄의철함수、중간점엄의철함수、단점엄의철함수사개정의，통과정의조건P1，연구조건P1소온함적등식관계，진이득도일개기출성정리일주밀성정리화일개상대조건교약적추론，최후장결과응용우약간불동류형적엄의철함수류，우기시s-철함수、궤하철함수、rp-철함수，득도타문소공유적일개특정성질，즉만족주밀성정리．
The author gives four definitions, that is generalized convex sets, generalized convex functions, intermediate-point generalized convex functions and endpoint generalized convex functions. Through define condition P~, the author study the equality relation which be contained with conditon P1. Furthermore, the author obtains a basic theorem-den~sity theorem and a lemma which condtion is relative weaker. At last, the author put these results on some different types of generalized convex functions such as s-convex functions, geometric convex functions and rP-convex functions. We will find that these generalized convex functions have a common characteristic properities, that is they satisfy the density theorem.
