集值映射的锥共轭映射

CONE-CONJUGATE MAPS OF SET-VALUED MAPS

本文对集值映射引进了一种在锥序意义下的共轭映射概念,说明了这种共轭映射是一种锥凸集值映射,而且它的图象、上图和水平集均是闭集,即具有闭性、上图闭性这样的连续性性质。另外文中还考虑了这种共轭映射的存在性及其它一些性质。

This paper introduced the concept of conjugate map of a set-valued map in thecone order sense. we showed the cone-conjugate map is a cone convex set-valued map and itsgraph, epigraph and level sets are closed, namely, the conjugate map has the continuousproperties in the closeness and epigraph closeness sense. Moreover, this paper discussed theexistence and some other properties of the conjugate maps.