平方s-凸函数及其性质

Square s-Convex Function and Its Properties

在凸函数和Godunova-Levin函数研究的基础上,针对平方凸函数的推广问题,分析从凸函数到s-凸函数的逻辑演变过程,提出了平方s-凸函数的概念,讨论了平方s-凸函数的判定定理及其运算性质,建立了平方s-凸函数的Jensen型不等式和Hadamard型不等式.

Based on the studying of convex function and Godunova-Levin function,the author analyzes the logical evolution process from convex function to s-convex function as to the issue of convex function extension,brings forward the concept of square s-convex function by scientific analogy method,discusses its several judgment theorems and operation properties,and sets up its Jensen-type inequality and Hadamard inequality.