混合单调算子的不动点定理及其应用

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.

The Fixed Point Theorems for Mixed Monotone Operators with Application

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.