Banach空间非单调算子方程新的不动点定理

New Fixed Point Theorems for a Class of Non-monotone Operators

利用锥理论和非对称迭代方法,研究了Banach空间一类既没有连续性条件也没有紧性条件而只满足某些序条件的非单调算子方程解的存在唯一性及迭代收敛性,得出了新的不动点定理并给出了此迭代的误差估计,所得结果是某些已知结果的本质改进和推广.

By using the cone theory and non-symmetry iteration method, in Banach Space, the existence and uniqueness of solutions of non-monotone operator equations without continuity and compactness conditions are studied, and the iteration sequence which converge to solution of operator equations and the error estimates are also given. A new fixed point is obtained. The results presented improve and generalize some corresponding ones.