局部强伪压缩算子的Ishikawa迭代的收敛性和稳定性

The Convergence and Stability of the Sequences of Ishikawa Iterative for Lipschitiz Strongly Locally Pseudo Contractive Mappings

设K是Banach空间X的非空闭子集 ,T :K →X是Lipschitz连续的局部强伪压缩算子 ,在没有条件limn→∞βn =0 ,limn→∞αn =0下 ,在Banach空间中讨论Lipschitz的局部强伪压缩算子不动点的具有误差的Ishikawa迭代序列的强收敛性 ,并在适当条件下证明了迭代序列的T稳定性 ,改进和发展了近期一些文献的结果 .

Let K be a nonempty closed subset of an arbitrary real Banach space X and T:K→X an Lipschitz continuous locally strongly pseudocontractive operators. In this paper, under certain condition without (lim)n→∞β_n=0,(lim)n→∞α_n=0, we prove that the Ishikawa methods with errors converges strongly to the fixed point of Lipschitz continuous locally strongly pseudocontractive operators. We also prove the stability of the iteration. The results improve and extend the recent results.