中文摘要：

对于Banach空间中一般的非线性方程，在一阶导数满足￡平均的仿射径向Holder条件下，讨论了经典牛顿迭代法的局部收敛性，得到了局部收敛性条件，同时证明了该方法的尺收敛阶至少为1＋p．在F＇满足L平均的Holder条件下，利用递推关系，给出了牛顿法的半局部收敛性定理．

英文摘要：

Under the affine radius Holder condition with L average for the first order Frechet derivative, the local convergence of classical Newton method for solving nonlinear equations was studied. Some local convergence conditions were given, the R-order of convergence was proved to be at least 1 ＋ p under those conditions. Under Holder condition with L average for the first order Frechet derivative, by the technique based on recurrence relation instead of majorant principle, the semilocal convergence theorem was established.