混合单调算子的不动点定理及其应用  

The Fixed Point Theorems for Mixed Monotone Operators with Application

作　　者：颜心力[1] 

机构地区：[1]西安冶金建筑学院,710055

出　　处：《应用数学》1991年第4期107-114,共8页Mathematica Applicata

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.

关 键 词：混合单调算子 半序空间 不动点 

分 类 号：O177.91[理学—数学]