一类广义凸函数及其等价刻画  

Generalized Convex Function and Its Equivalent Characterization

作　　者：蔡威[1] 金成铭[1] 

机构地区：[1]空军第一航空学院基础部,河南信阳464000

出　　处：《数学的实践与认识》2017年第13期233-237,共5页Mathematics in Practice and Theory

摘　　要：引入了一个广义凸函数一高阶强Pre-invex函数,它是Guneer-Bhatia介绍的高阶强凸函数的一种推广.在此基础上,讨论并证明了高阶强Pre-invex函数的一些等价刻画,这些结论是Guneer-Bhatia给出结论的推广,扩大了凸函数的应用范围.In this paper, we introduce a generalized convex function, called higher order strong Pre-invexity function, which is generalization of the definition for higher order strong convex function by Guneer Bhatia in literature [5]. Based on this, we discuss and prove some equivalent characterizations about higher order Pre-invex function. This work generalize results in literature [5] and extend applied ranges of convex function.

关 键 词：高阶强凸函数 高阶强Pre—invex函数 等价刻画 

分 类 号：O174.13[理学—数学]