一致似凸函数和一致半严格似凸函数

Uniformly Convexlike and Uniformly Semistrictly Convexlike Functions

H.H.artwig和F.A.Behriger研究了一致似拟凸函数的性质。本文进一步定义和讨论了一致似凸函数和一致半严格似凸函数及其性质,特别是广义Karamardian定理对于一致半严格似凸函数成立。

H.Hartwig[3] and F.A.Behringer[1] have recently studied some properties of uniformly quasiconvexllke functions. In this paper we further define uniformly semistrictly convexlike and uniformly convexlike functions and discuss their properties. In particular, this paper shows that generalized Karamardian's theorem is tenable with respect to uniformly semistrictly convexlike functions.