Banach空间一类新反向混合单调算子的不动点定理

Fixed Point Theorems of Some New Anti-mixed Monotone Operator in Banach Space

运用锥与半序理论和非对称迭代方法,讨论半序Banach空间一类反向混合单调算子的不动点定理,并给出了迭代序列收敛于解的误差估计,并推广讨论了非反向混合单调算子的不动点定理,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 non-symmetry iteration method, it is studied 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 converge to solution of operator equations and the error estimates are also given. For its application, it is mainly studied the existence and uniqueness of solutions of non-anti-mixed monotone operator system of equations. The results presented here improve and generalize some corresponding results for mixed monotone operators.