局部凸拓扑空间中凝聚映象的不动点定理

Fixed Point Theorems of Condensing Operator in Locally Convex Topological Vector Spaces

利用拓扑度理论讨论了局部凸拓扑向量空间中凝聚映象的不动点问题,首先证明了凝聚映像中的Leray-Shauder定理,然后应用此定理在局部凸拓扑向量空间中进一步推广了Altman定理,从而获得了一些更为广泛的不动点定理,所得结果是已知结果的本质改进与推广.

In this paper, by using topological degree theory, we discuss fixed point theorems of condensing operator in locally con- vex topological vector spaces. First, we prove Leray-Shauder fixed point theorem of condensing operator. From this theorem we general- ize the famous Altman theorem in locally convex topological vector spaces. Then some more generalized fixed point theorems are ob- tained, which improve and generalize some corresponding ones.