凸函数理论的最新进展  

Some Recent Developments in the Theory of Convex Functions

作　　者：匡继昌[1] KUANG Jichang(Department of Mathematics, College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan, 410081, P.R.China)

机构地区：[1]湖南师范大学数学与计算机科学学院数学系,湖南长沙410081

出　　处：《广东第二师范学院学报》2018年第3期14-24,共11页Journal of Guangdong University of Education

摘　　要：引进了加权幂平均凸函数的新概念,它包括了古典的凸函数的多种推广,并建立了相应的广义Schur、Jensen和Hermite-Hadamard不等式,还介绍了凸函数概念的其他推广及其相应的凸性不等式.In this paper,we introduce the new notion of convex functions for weighted power means. It includes various generalizations of convex functions as the special cases. The corresponding generalized Schur,Jensen and Hermite-Hadamard inequalities are also established. Some recent developments of convex function theory and its inequalities are also given.

关 键 词：凸函数 加权幂平均 凸性不等式 

分 类 号：O178[理学—数学]