Banach乘积空间中映射的不动点存在唯一性及在泛函方程近似解法中的应用

一、引言 非线性方程迭代解法(如Newton法,最速下降法)推广到方程组,收敛条件相当复杂(如需算Jacobi逆矩阵),其大范围内收敛条件,更难建立。用Banach压缩映象原理来解各种函数方程(如微分、积分、泛函微分、代数方程等),关键在于判明是否存在小于1的Lipschitz常数,有时,很难实现。在1]中,Hilbert空间内对有界线性算子用Seidel迭代法,要保证算子正定、对称、逆算子存在等很强假设,再化成另一线性算子的一般迭代来证

EXISTENCE AND UNIQVENESS OF THE FIXED POINT FOR A MAPPING ON PRODUCT BANACH SPACE AND APPLICATIONS TO SOLVING A FUNCTIONAL EQUATION BY APPROXIMATE METHOD

We consider some convergance criteria for Gauss-Seidel and Jacobi iterations of amapping on a product Banach space, and estimate their speed of convergence. The basicresults may be applied to solving a functional equation by the approximate method.