几何s-凸函数及其性质  

Geometric s-Convex Function and Its Property

作　　者：宋振云[1] 

机构地区：[1]湖北职业技术学院机电工程学院,湖北孝感432000

出　　处：《山西师范大学学报（自然科学版）》2016年第1期1-5,共5页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：湖北省教育科学"十二五"规划项目(2014A060)

摘　　要：函数凸性及其广义凸性是函数的重要性质之一,对凸函数进行分类和推广是研究函数凸性及其广义凸性的一个重要途径.在研究凸函数、Godunova-Levin函数、P-函数和s-凸函数的基础上,针对几何凸函数的推广问题,提出了几何s-凸函数的概念,通过分析几何s-凸函数的凸性特征,给出了几何s-凸函数的若干判定定理和运算性质,建立了几何s-凸函数的Jensen型不等式和Hadamard型不等式.几何s-凸函数概念的建立为研究新的凸函数和拓展凸函数概念开辟了一条新途径.The convexity and general convexity are significant property of function. It is an important method for researching the convexity and its general convexity to classify and popularize convex function. Based on studying convex function,Godunova-Levin function,P-function and s-convex function,the concept of geometric s-convex function is proposed,several judging theorem and operation property of geometric s- convex function is offered by analyzing the convexity character of geometric s- convex function,and Jensen inequation and Hadamard inequation of s-geometric convex function is established,which can be regarded as a new way into exploring new convex function and expanding the concept of convex function.

关 键 词：s-凸函数 几何s-凸函数 判定定理 运算性质 Jensen型不等式 

分 类 号：O178.1[理学—数学]