期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2009
卷号：2009
DOI：10.1155/2009/615107
出版社：Hindawi Publishing Corporation
摘要：Let 𝐸 be a real Banach space, and 𝐾 a closed convex nonempty subset of 𝐸.
Let 𝑇1,𝑇2,…,𝑇𝑚∶𝐾→𝐾 be 𝑚 total asymptotically nonexpansive mappings. A
simple iterative sequence {𝑥𝑛}𝑛≥1 is constructed in 𝐸 and necessary and sufficient
conditions for this sequence to converge to a common fixed point of {𝑇𝑖}𝑚𝑖=1 are given. Furthermore, in the case that 𝐸 is a uniformly convex real Banach space,
strong convergence of the sequence {𝑥𝑛}∞𝑛=1 to a common fixed point of the family
{𝑇𝑖}𝑚𝑖=1 is proved. Our recursion formula is much simpler and much more applicable than those recently announced by several authors for the same problem.
