一类反向混合单调算子方程组的迭代求解

The Iterative Solution of the System for a Class of Anti-Mixed Monotone Operator Equations

在序Banach空间中,利用锥与半序理论和非对称迭代技巧,研究一类反向混合单调算子方程组{A(x,x)=x,B(x,x)=x}解的存在与唯一性,给出了收敛于算子方程组解的逼近迭代序列和误差估计,进而获得了反向混合单调算子方程A(x,x)=x唯一解及其解的逼近迭代序列和误差估计,并改进和推广了有关文献的相应结果。

In ordered Banach spaces, by the cone and partial ordering theory, and non-symmetry iterative tech- niques, the existence and uniqueness of the solution for the system of a class of anti-mixed monotone operator system are studied, and the iterative sequences which converge to the solution for system of operator equations and the error estimations are given, and the iterative solution, the iterative sequences which converge to the solution and the error estimations of the anti-mixed monotone operator equation A（x,x）= x are also obtained. The results of some references are improved and extended.