CQ Method for Strictly Pseudo-Contractive Mapping

This paper obtains a strong convergence theorem for k-strictly pseudo-contractive mapping under the framework of Hilbert spaces using CQ method. Due to the fact that non-expansive mapping is only 0-strictly pseudo-contractive, the main result obtained in this paper extends the corresponding main result of Nakajo-Takahashi from non-expansive mapping to k-strictly pseudo-contractive one, where k∈[0,1).     

拟非扩张算子序列Ishikawa迭代过程的构造及收敛性

以一致凸Banach空间的有界闭凸集上的拟非扩张算子的不动点问题进行了研究。得出了该类算子有公共不动点的充分条件，并构造了相应的Ishikawa迭代序列使之收敛于其公共不动点。此结果是近期相关结论的推广。     

Picard Approximation of Fixed Points of Nonexpansive Mappings

LetXbeaBanachspaceandCbeaconvexsubsetofX .T :X→Cisanonexpansivemapping ,thatis ,Tx -Ty ≤x - y forallx ,y∈X .Now ,westudythefollowingiterativeprocessforx0 ,un∈C ,xn 1=Snxn, ( 1 )whereSn =αn0 I αn1T αn2 T2 … αnkTk γnun,andαni≥ 0 ,0 <α≤αn