Hausdorff局部凸线性拓扑空间中多值拟非扩张映射的不动点定理

Fixed Point Theorem for Multivalued Mapping of Quasi-nonexpansive in Locally Convex Hausdorff Topological Vector Space

本文证明如果K为Hausdorff局部凸线性拓扑空间X的具有正规结构的非空有界弱紧凸子集,则K上的具有值为紧凸集的多值拟非扩张映射均有不动点。

In this paperl a main result is obtained.Let X be a locally convex Hausdorff topological vector space, K a nonempty bounded, weakly compact, convex subset of X which posseses normal structure, and let f be a multivalued quasi-nonexpansive mapping of K into CC(K), then f has a fixed point in K.