φ-序压缩算子的不动点定理  

Fixed Point Theorems for φ-Ordered Contractive Operators

作　　者：尹建东[1] 尹国昌[2] 

机构地区：[1]南昌大学数学系,江西南昌330031 [2]江西师范大学体育系,江西南昌330022

出　　处：《数学研究》2010年第2期171-177,共7页Journal of Mathematical Study

基　　金：江西省自然科学青年基金资助项目(2008GQS0071)

摘　　要：2005年,张宪在Banach空间中通过其中的锥所定义的半序引进了序压缩算子,证明了几个相应的定理.但是在一般的度量空间中,能否定义序压缩算子,能否得到类似的结论呢?本文在度量空间X中,通过X上的泛函φ所定义的半序,引进了φ-序压缩算子,并且得到了相应的不动点定理.In 2005, Zhang xian introduced the notion of ordered contractive operator and obtained some fixed point theorems in Banach space via a partial order decided by a cone. But can the same notion of ordered contractive operator be introduced in a metric space？ Whether the analogous results still hold？ In this paper, the ordered contractive operator is introduced and some fixed point theorems are proved in a complete ordered metric space on which the partial order is induced by a function.

关 键 词：φ-序压缩算子 不动点 完备度量空间 

分 类 号：O177.91[理学—数学]