基于对称迭代法的二元算子方程解的存在性研究

The existence study based on the solution of binary operator equation of the symmetric iteration method

运用锥与半序理论和对称迭代方法,讨论了一类不具有反向混合单调性的二元算子方程解的存在惟一性,且给出了迭代序列收敛于解的误差估计.并把所得结论应用于二元算子方程组,所得结果改进和推广了反向混合单调算子方程某些已知的相应结果.

Using the cone and partial theory and symmetry iteration method, this paper studies the existence and uniqueness of solutions of a class of binary operator equation without anti-mixed monotone condition, and the iteration sequences which converge to solution of operator equations and the error estimates are also given. The conclusion applies to the binary operator equations. The results presented here improve and generalize some corresponding results for anti-mixed monotone operators.