Iterative Solutions of Nonlinear Equations of the Strongly Accretive Type
Iterative Solutions of Nonlinear Equations of the Strongly Accretive Type
复制标题
强累加型非线性方程的迭代解
DOI：
10.1002/mana.19981890105
复制
发表时间：
1998
影响因子：
1
通讯作者：
C. Chidume
中科院分区：
文献类型：
--
作者：
C. Chidume
设E是实的q一致光滑的Banach空间。设T是E中具有开域D(T)的强伪压缩映射，进一步假设T在D(T)中有不动点。在T上不同的连续性假设下，证明了Mann迭代过程和Ishikawa迭代方法都强收敛于T的唯一不动点。相关结果讨论了含强增生映象的非线性算子方程的迭代解。文中还给出了显式误差估计。
Let E be a real q‐uniformly smooth Banach space. Suppose T is a strongly pseudo‐contractive map with open domain D(T) in E. Suppose further that T has a fixed point in D(T). Under various continuity assumptions on T it is proved that each of the Mann iteration process or the Ishikawa iteration method converges strongly to the unique fixed point of T. Related results deal with iterative solutions of nonlinear operator equations involving strongly accretive maps. Explicit error estimates are also provided.