一类新条件下的渐近非扩张映象迭代算法的收敛性

Convergence of Iterative Algorithm with an Asymptotically Nonexpansive Mapping under a Class of New Assumptions

首次引进新的假设条件Ф≠F(T)=F(T2)=…=F(Tn)=…,其中F(T)是渐近非扩张映象T的不动点集.在自反Banach空间的框架下,获得了渐近非扩张映象T的迭代序列强收敛于其不动点的结论.

A new assumption Ф≠F（T）=F（T2）=…=F（Tn）=… is originally introduced,where F（T） is the fixed point set of an asymptotically nonexpansive mapping T.The sufficient conditions for the iterative sequence strongly converging to a fixed point of T are obtained in Banach spaces.