赋范空间中渐近伪压缩映象不动点的迭代逼近

摘要

设X是赋范线性空间,D是X的非空子集. 设T∶D→X是一个一致L-Lipschitz的渐近伪压缩映象,F(T)表T的不动点集且F(T)非空. 在迭代参数{αn}和{βn}的适当假设下,证明了修改了的具有误差项的Ishikawa和Mann迭代过程强收敛于T的不动点q. 几个相关结果处理赋范空间中渐近非扩张映象不动点的迭代逼近问题. 所得结果改进和推广了Chang, Park和Cho, Geobel和Kirl, Liu以及Schu等人的相关结果.%Let X be a normed linear space, D be a nonempty subset of X and T∶D→X be a uniformly L-Lipschitz asymptotically pseudo-contractive mapping. F(T) denotes the set of all fixed points of T and F(T) is nonempty. Under some suitable assumptions on the iteration parameters {αn} and {βn}, we have proved that the modified Ishikawa and Mann iterative processes with errors for T converge strongly to the fixed point q of T. Several related results deal with iterative approximation problem of fixed point of asymptotically nonexpansive mappings in normed linear space. The results presented in this paper improve and extend those corresponding ones by Chang, Park and Cho, Geobel and Kirk, Liu and Schu and others.