基于对称迭代的反向混合单调算子方程组解的存在惟一性

Existence and uniqueness of solutions of some anti-mixed monotone operator systems of equations based on symmetric iteration

运用锥与半序理论和对称迭代方法,讨论半序Banach空间一类反向混合单调算子方程组解的存在惟一性,并给出了迭代序列收敛于解的误差估计,同时讨论了非反向混合单调算子方程组解的存在惟一性。所得结果改进和推广了混合单调算子方程某些已知相应结果。

Using the cone, partial theory and symmetry iteration method, this paper dealt with the existence and uniqueness of solutions of a class of anti-mixed monotone operator system of equations in Banach spaces. And the iteration sequences which related to solution of operator equations and the error estimates were also given. For its application, an emphasis was put on the existence and uniqueness of solutions of non-anti-mixed monotone operator system of equations. The results presented here improve and introduce some corresponding results obtained by mixed monotone operators.