Banach空间中非单调二元算子方程的迭代解

Iterative solution for non monotone binary operator equations in Banach spaces

利用非线性泛函分析中的单调迭代方法和锥与半序理论 ,讨论Banach空间不具有单调性的二元算子方程解的存在性与唯一性 ,并给出收敛于方程的解的迭代序列和误差估计 .文中的算子不具有任何连续性和紧性 ,也不要求算子是某序区间上的自映象 .

With using the monotone iterative method and cone and partial ordering theory in nonlinear functional analysis,the existence and uniqueness of solution for nonmonotone binary operator equations in Banach spaces are discussed.And the iterative sequences which converge to solution of operator equations and the error estimates are also given.In this paper the operators do not possess any continuity and compactness,and that the operator is a self mapping on ordering interval is not required.The results presented here improve and generalize some corresponding results for iterative solution of mixed monotone operator equations and unary operator equations.