Banach空间中一类非单调算子方程解的存在性定理

The Existence of the Solutions of Some Non-monotone Operator Equations in Banach Space

运用锥理论与非对称迭代方法,得到了Banach空间不具有单调性、连续性和紧性条件的一类算子的不动点的存在唯一性,并给出了迭代序列收敛于解的误差估计,所得结果改进和推广了增(减)算子方程的某些已知结果.

By using the core theory and non-symmetric iterative method, it is studied the existence uniqueness of solutions of some operator equations without monotone and continuity and compactness conditions in Banach spaces. And the iterative sequences which converge to solution of operator equations and the error estimates are also given. The results presented here improve and generalize some corresponding results for increasing （decreasing） operator equations.