banach不动点定理的推广.doc

Banach不动点定理的推广

原创

摘  要：本文先介绍了Banach不动点原理即压缩映射原理，再将映射从 到 的， 是完备的，改为在它的子集上,如:开球，闭球，有界闭集，紧集等，添加某些条件及其限制，得到定义在上述子集上的不动点定理和推论,并将文 中的例2给予了正确证法。
关键词：度量空间; 完备度量空间; 不动点; 压缩映射; Banach不动点原理

The extensions of Banach immovable point

Abstract:  In this paper, at first it presents Banach immovable point principle i.e. contraction mapping principle, then let a mapping from X to X which is a complete metric space change into its subsets .Such as: open sphere, closed sphere, bounded closed set, compact set and so on, add to some conditions and limititation, so the theorem of fixed point and generalization which are defined in the above subsets can be obtained. At last giving the right proof of example two of the paper .
Keywords: metric space; complete metric space; fixed point; contraction mapping; Banach immovable point;