Banach空间中X=Cx+d型线性方程组解的存在性与唯一性

Existence and Uniqueness of Solution Linear Equations of X=Cx+d in Banach Space

利用不动点定理将n阶线性方程组X=Cx+d在范数‖·‖1的列范数下解的存在性与唯一性推广至范数‖·‖1的行范数、范数‖·‖p和范数‖·‖∞,并将这一性质推广至无限阶线性方程组.

In this paper,it is proved that the existence and uniqueness of solution in line norm of norm ‖·‖1 extend to row norm of norm ‖·‖1,norm ‖·‖p and norm ‖·‖∞ by means of theorem of fixed.Meanwhile,the property is extended to linear equations by infinite.