摘要
本文在一类新型假设条件下,建立一种新的方法——非对称迭代法,解决了半序空间中惯用的对称迭代法所无能为力的问题.引入半序距离空间概念,对于二元对称压缩算子,给出了几类具有代表性的不动点定理,拓广了Hilbet投影距离概念,获得较以往更为广泛的不动点定理.最后给出若干应用.
Under certain supposed conditions, a new method-non-symmetry iteration method has been worked out. It proves to be effective in solving problems which cannot be solved by using the symmetry iteration method. The author introduces a conception of semi-order distance space and obtains a few typical fixed point theorems for the two-element symmetric contracted operator. Furthermore, the author expands the conception of Hilbet projective metric. and sets a new fixed point theorem which is far more useful than the old one. In conclusion several examples of the application of the new method are given.
出处
《应用数学》
CSCD
北大核心
1991年第4期107-114,共8页
Mathematica Applicata
关键词
混合单调算子
半序空间
不动点
Semi-order space
Mixed monotone operator
Non-symmetric iteration
