Hilbert空间上无穷可数族非自射k-严格伪压缩映象之公共不动点的带误差逼近

Approximation to Common Fixed Points of Infinite Countable Family of k-Strictly Pseudocontractive Nonself-mappings with Errors

利用Petryshyn不等式引理和无穷可数族W-映象技巧,证明了涉及无穷可数族非自射k-严格伪压缩映象{Si:C→H}i∞=1的含误差的显式迭代算法的强收敛性,从而在H ilbert空间将已有的自射非扩张映象的迭代算法推广到非自射k-严格伪压缩映象的迭代算法.

By way of the Petryshyn inequality lemma and W-mapping technique,the author proves that an explicit iterative algorithm with infinitely many k-strictly pseudocontractive mappings converges strongly to a common fixed point of the mappings.In the setting of Hilbert spaces,the strong convergence theorem extends some recent result from explicit iteration of nonexpansive self-mappings into explicit iteration of k-strictly pseudocontractive nonself-mappings with errors.