半p-拟凸函数的一些性质及应用

Some Properties and Application of Semi p-Quasiconvex Function

本文在半p-不变凸集和半(p,r)-前-不变凸函数的基础上,提出了与半(p,r)-前-不变凸函数相关的一类广义凸函数——半p-拟凸函数,探讨了它与一些熟知的广义凸函数间的关系和它的有关性质,以及这类广义函数的局部极小点与全局极小点的关系.

In the article, it introduces and studies a new class of generalized convex function--semi p-quasiconvex func- tion, which includes p-quasiconvex function as a special case. It discusses some properties for the semi p-quasiconvex functions. As an application, it shows some relations between the local minimum point and the global minimum points for the semi p-quasi-convex and strongly semi p-quasiconvex functions.