二元算子方程组的迭代求解方法

Iterative Solutions Methods for Systems of Two Binary Operator Equations

利用锥理论和单调迭代方法,本文在Banach空间中对三类二元算子方程组的求解进行了探讨,利用较简捷的条件得出方程组的唯一解和迭代逼近式及误差估计式并推广到了n元算子方程组的情形,得到相应结果．

Using the cone and monotone iterative theory, the existence and uniqueness of solutions for three classes of systems of two binary operator equations in Banach space are discussed, and the error estimations for the convergent iterative sequence are also given. As a generalization, the solutions for some classes of n variable operator equations are also discussed.