一致半压缩映像的Ishikawa和Mann迭代过程的收敛性问题(英文)

On the Convergence Problems of Ishikawa and Mann Iterative Processes for Uniformly Hemi-Contractions

设E为赋范线性空间,D是E的非空子集,T:DE为Lipschitz连续和一致半压缩映像,在αn0,βn0和∑∞1αn=∞的条件下,证明了一致半压缩映像的不动点的Ishikawa和Mann迭代方法的强收敛性.

Let E be a normal linear space, D be a nonempty subset of E and T：D→E be a Lipschitz and uniformly hemi-contractive mapping. Under condition, αn→0,βn→0,and ∑1an=∞, it is proved that the Ishikawa methods converges strongly to the fixed point of Lipschitz uniformly hemi-contractive mapping