凸度量空间内渐近拟非扩张映射不动点的迭代

2001年和2002年Liu Qihou推广了Petryshgh和Williamson,Ghosh和Debnath分别在1973年和1977年的结果,在Banach空间和一致凸Banach空间证明了Ishikawa迭代序列和带误差的Ishikawa迭代序列收敛于渐近拟非扩张映射不动点的若干充要条件.笔者在凸度量空间内,定义了带误差的Ishikawa迭代程序,并且证明了带误差的Ishikawa迭代程序收敛于渐近拟非扩张映射不动点的若干充要条件.该结果统一和推广了近期文献中的许多已知结果.

Convergence of Ishikawa Type Iterative Sequence With Errors for Asymptotically Quasi-nonexpansive Mappings in Convex Metric Spases

Liu Qihou, in 2001 and in 2002, extended the results of Petryshgh and Williamson, Ghosh and Debnath respectively in 1973 and in 1977, proved some sufficient and necessary condition for Ishikawa iterative sequence and for Ishikawa iterative sequence with error member of asymptotically quasi-nonenpansive mappings to converge to fixed poind in Banach space and in uniform convex Banach space. In convex metric spaces,the Ishikawa iteration process with errors is defined for asymptotically quasi-nonexpansive mappings.Some sufficient and nevessary conditions proved for the iterative schene converges to the fixed point of the asymptotically quasi-nonexpansire mappings.These results qeneralize and unify many important known results in recent literature.