抽象凸空间上弱KyFan点的存在性及其等价描述

Existence of weak Ky Fan point and it's equivalence descriptions in abstract convex space

为获得非紧集上不具有任何连续性函数的弱KyFan点的存在性及其等价描述,利用KKM方法和非线性分析中经典的不动点各种等价描述证明思想方法,得到空间不具线性结构、函数定义域不具紧性和函数不具任何连续性的条件下弱KyFan点的存在性及其等价性描述的一些结果.结果表明:弱KyFan点、弱KyFan截口点和弱Fan Browder不动点等的存在性等价.若增加空间的线性结构、定义域的紧性和函数的半连续性这些条件就能得到经典的KyFan点、KyFan截口点和Fan Browder不动点的存在性及其相应等价描述,是研究结论的特例.

In order to achieve the existence of weak KyFan points and it's equivalence descriptions for functions defined on non-compact sets and the functions without any continuous properties, this study proved that the existence of weakly Ky Fan points and it's equivalence descriptions for functions whose domain space without linear structure and without compactness, and itself without any continuous properties by using KKM approaches and the known checking approaches of equivalence descriptions of fixed point on nonlinear analysis. The results show that the existence of weakly Ky Fan points, the existence of Ky Fan cut points and the existence of weakly Fan Browder fixed points are equivalent. The known existences and equivalences of Ky Fan points, Ky Fan cut points and Fan Browder fixed points will be obtained if we give additional conditions of linear structure of the domain space, the compactness of the domain set and the lower semi-continuity for the function, thus the known results are the specialities of our outcomes in this paper.