A lemma is obtained which guarantees that non-expansive mappings on contractive spaces have fixed points. An example shows that Schauders's fixed point theorem cannot be extended to contractive spaces, but a theorem for contractive spaces, analogous to a result of B. N. Sadovskii on convex spaces, is derived from the lemma. Finally, some local results for ?μ-chainable contractive spaces are given.
展开▼
机译：获得一个引理，该引理保证紧缩空间上的非膨胀映射具有固定点。一个例子表明，Schauders的不动点定理不能推广到收缩空间，但是收缩空间的一个定理类似于引理上B. N. Sadovskii在凸空间上的结果。最后，给出了关于？μ可链收缩空间的一些局部结果。
展开▼
