玉林师范学院学报
玉林師範學院學報
옥림사범학원학보
Journal of Yulin Teachers College
2007年
5期
1-4,14
,共5页
E-凸函数%E-对数凸函数%E-Jensen不等式%E-对数Jensen不等式
E-凸函數%E-對數凸函數%E-Jensen不等式%E-對數Jensen不等式
E-철함수%E-대수철함수%E-Jensen불등식%E-대수Jensen불등식
E-convex function%E—logarithmic convex function%E-jeilsen type inequality%E—logarithmic Jensen type inequality
本文根据E.A.Youness提出的E-凸集和E-凸函数的定义,基于广义凸性基本结论,对判断可微函数为E-凸函数的两个充要条件给予了证明,并提出了E-Hesse 矩阵、E-时数凸函数,且提出并证明了E-Jensen不等式和E-对敷Jensen不等式.
本文根據E.A.Youness提齣的E-凸集和E-凸函數的定義,基于廣義凸性基本結論,對判斷可微函數為E-凸函數的兩箇充要條件給予瞭證明,併提齣瞭E-Hesse 矩陣、E-時數凸函數,且提齣併證明瞭E-Jensen不等式和E-對敷Jensen不等式.
본문근거E.A.Youness제출적E-철집화E-철함수적정의,기우엄의철성기본결론,대판단가미함수위E-철함수적량개충요조건급여료증명,병제출료E-Hesse 구진、E-시수철함수,차제출병증명료E-Jensen불등식화E-대부Jensen불등식.
According to the definitions of E-Convex set and E-convex function presented by E.A.Youness;this paper based on Some basic conclusions of the generalized convexity.In this paper,we obtain two sufficient and necessary conditions of the judging differentiable function whether it be E-convex function or not be given,and we present four new conclusions--the E-Hessian matrix,E-logarithmic convex function,the E-Jensen type inequality and E-logarithmic Jensen type incquality.
