一类非混合单调算子的不动点定理

Fixed Point Theorems for a Class of Non-mixed Monotone Operators

利用锥理论和非对称迭代方法,讨论了Banach空间中不具有单调性、连续性和紧性条件而只满足某些序条件的非混合单调算子方程解的存在唯一性及迭代收敛性,并给出了此迭代的误差估计,所得结果改进和推广了混合单调算子方程的某些已知结果.

By using the cone theory and non - symmetry iteration method, the existence and uniqueness of solutions of non-mixed monotone operator equations without monotonicity, continuity or compactness conditions are studied, and the iteration sequences which converge to solution of operator equations and the error estimates are also given. The results improve and generalize some known results on mixed monotone operator equations.