Hilbert空间框架下严格渐近伪压缩映像的强收敛定理

Strong Convergence Theorems for Asymptotically Strictly Pseudocontractive Maps in Hilbert Spaces

中文关键词:  非扩张映像  严格渐近伪压缩映像  Hilbert空间  投影

英文关键词:nonexpansive mappings  strictly pseudocontractive mappings  Hilbert spaces  projection.

中文摘要:

      Mann迭代程序即使在Hilbert空间框架下对于非扩张映像仍然没没有强收敛结果. 本文在Hilbert空间框架下引入了修正的Mann迭代程序对于严格渐近伪压缩映像得到了强收敛性. 本文的结果改进和推广了Kim, Xu$^{[4]}$, Nakajo, Takahashi$^{[3]}$和其他一些人相应的结果.

英文摘要:

      The Mann iterations have no strong convergence even for nonexpansive mappings in Hilbert spaces. The aim of this paper is to propose a modification of the Mann iterations for strictly asymptotically pseudocontractive maps in Hilbert spaces to have strong convergence. Our results extend those of Kim, Xu$^{[4]}$, Nakajo, Takahashi$^{[3]}$ and many others.