Banach空间一类非线性算子方程解的存在唯一性

Existence and Uniqueness of the Solutions of Some Non-linear Operator Equations in Banach Space

利用锥理论和非对称迭代方法,研究了半序Banach空间一类不具有连续性和紧性条件的非线性算子方程A(x,x)+u0=Bx解的存在唯一性,并给出迭代序列收敛于解的误差估计,所得结果是某些已有结果的本质改进和推广。非对称迭代方法是解决微积分方程的又一有效方法,它能够解决半序空间中对称迭代法无能为力的问题。

Using the cone theory and non - symmetric iteration method, the existence and uniqueness of the solu-tions of a class of non ＂linear operator equations A （x,x） ＋ uO = Bx without continuity and compactness conditions are studied. And the error estimates that the iterative sequences converge to solutions are also given. The resuits presented here are of the improvement and generalization of some corresponding results. Non - symmetric iteration method is another efficient method of solving the integral equation and the problem that cant be dealt with by using the symmetric iteration method in the semi -ordered space.