各种抽象凸结构的统一描述

Unified Description of Various Abstract Convex Structure

空间的凸性在不动点理论和连续选择理论以及优化问题中起着十分重要的作用。国内外专家学者对线性凸的结构和其内在性质作了深入研究,提出了各种各样具有广泛意义的凸结构。本文发现一种更具一般意义的抽象凸结构,并证明了它包含前面的各种凸结构,从而可以对这些凸结构进行统一描述。

Space convexity plays a very important role in fixed point theory, continuity selection theory and optimal problems. Exports and scholars of China and other countries have made deep researches on linear convex structures and their inner properties and, have put forward variety of extensively meaningful convex structures. This paper is to give out an abstract convex structure in more general sense and, to prove it comprises previous various convex structures and so, to work out an unified description for these previous all convex structures.