摘要
本文证明了 Ｋｙ Ｆａｎ定理［１］对定义在 Ｂａｎａｃｈ空间中含有内点的有界闭凸子集上的１－集－压缩映象正确．１－集－压缩映象类包含凝聚映象、非扩张映象、半压缩映象、局部几乎非扩张映象和其它映象．作为定理的应用，得到了一些非自映象在许多众知边界条件下的不动点定理，改进和推广了许多作者的最近结果．
In this paper, we will prove that Ky Fan's Theorem[1] is true for 1-set- contractive maps defined on a bounded closed convex subset K in a Banach space with int K ≠0. This class of 1-set-contractive map includes condensing maps, non- expansive maps, semicontractive maps, LANE maps and others. As applications of our theorems, some fixed point theorems of non-self-maps are proved under various well-known boundary conditions. Our results are generalizations and improvements the recent results obtained by many authors.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2001年第5期843-848,共6页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目
山东省自然科学基金资助项目
