广义压缩映射的一种连续方法与广义扩张映射的不动点性质（英文）  

A Continuation Method for Generalized Contractive Mappings and Fixed Point Properties of Generalized Expansive Mappings

作　　者：王宏勇[1] 

机构地区：[1]南京财经大学应用数学学院,南京江苏210023

出　　处：《数学进展》2017年第1期111-121,共11页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.11071152)

摘　　要：本文给出了一类广义压缩映射的一种连续方法,在完备度量空间中建立了一类非自映射的一个同伦定理.引入了一类广义扩张映射,给出了它们的不动点定理,并在一定的条件下,证明了这些不动点构成了Banach空间中一个不可数的闭集.A continuation method for a class of generalized contractive mappings is given, which establishes a homotopy theorem for a class of non-self mappings in a complete metric space. In addition, a type of generalized expansive mappings is introduced and the corresponding fixed point theorem is proved. Finally, the analytical properties of the fixed points of such a generalized expansive mapping are investigated and it is proved that the set of such fixed points is uncountable and closed in a Banach space.

关 键 词：连续方法 广义压缩映射 不动点 广义扩张映射 

分 类 号：O177.91[理学—数学]