混合单调算子方程解的存在唯一性定理及应用

Existence and Uniqueness Theorems of the Solution To Mixed Monotone Operator Equation and Their Applications

一般来说,凡在半序空间用迭代法研究算子方程的解时均采用对称迭代,事实上,一般的对称迭代并不收敛或者不收敛于算子方程的解。本文构造了各种形式的非对称迭代,获得一系列混合单调算子方程解的存在与唯一性定理,并给出它的一些应用。

Generally speaking,in partially oraered space,symmetric iteration is adopted,while the solution to operator equation is studied with iteration.In fact,the sequence from symmetric iteration does not necessarily converge or does not converge to the solution of operator equation.This paper presents all sorts of nonsymmetric iterations and obtains existence and uniqueness theorms of solution to mixed monotone operator equation and provides their applications.