一类非单调二元算子方程的可解性

Solveability Theorems of a Non-monotone Binary Operator Equation

在非单调二元算子A不具有连续性以及保序关系的情况下,利用锥理论和半序方法讨论了Banach空间中一类二元算子方程Lx=A(x,y)的解的存在性问题,引入"可比较"等新的概念,在新的条件下,研究其迭代序列的逼近情况,推广并得到了一些新的定理。

The theorem of cone and the techniques of partial order theory are used to discuss the solveability theorems of an operator equation Lx=A（x,y） in Banach space,where non-monotone operator A needn＇t to be continuous and satisfied some order conditions.In some new conditions,it studied the approximation for the iterative sequences by introducing new concept such as ＂comparison＂,and obtained some new theorems.