h-凸函数(英文)  

h-Convex Functions

作　　者：焦合华[1] 

机构地区：[1]长江师范学院数学系,重庆涪陵408003

出　　处：《昆明理工大学学报（理工版）》2007年第4期114-119,共6页Journal of Kunming University of Science and Technology(Natural Science Edition)

基　　金：the National Science Foundation of China(Grant 10171118) and the Educational Science Foundation of Chongqing,Chongqing of China(KJ051307,041302)

摘　　要：针对凸函数,s-凸函数,Godunova-Levin函数和P-函数定义的特点,引入了一类新的广义凸函数——h-凸函数,它推广了凸函数、s-凸函数、Godunova—Levin函数和P-函数的概念;接着,讨论了h-凸函数的一些有用性质;最后,利用h函数的上(下)积性给出了h-凸函数在不等式中的2个应用,推广了Schur和Jensen不等式.Based on the characteristics of convex functions, s - convex function, Godunova - Levin function and P - function, a new class of generalized convex function of h - convex is introduced, which generalizes the convex function, s - convex function, Godunova - Lcvin function and P - function： then, some important properties of h - convex function are discussed. Finally, by using super （sub） multiplicativity of h -function two applications for h -convex function to inequalities are presented,which generalizes Schur and Jensen inequalities.

关 键 词：凸函数 积性函数 SCHUR不等式 JENSEN不等式 

分 类 号：O174.13[理学—数学]