TY - JOUR
T1 - Approximation of the Nearest Common Fixed Point of Asymptotically Nonexpansive Mappings in Banach Spaces
AU - Wang , Xiongrui
JO - Communications in Mathematical Research 
VL - 4
SP - 369
EP - 377
PY - 2021
DA - 2021/05
SN - 27
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19080.html
KW - asymptotically nonexpansive mapping, sunny nonexpansive retraction, uniformly Gâteaux differentiable, weakly sequentially continuous duality.
AB - <p style="text-align: justify;">In this paper, the iteration $x_{n+1} = α_ny + (1 − α_n)T^{k(n)}_{i(n)} x_n$ for a family
of asymptotically nonexpansive mappings $T_1, T_2, · · · , T_N$ is originally introduced in
a uniformly convex Banach space. Motivated by recent papers, we prove that under
suitable conditions the iteration scheme converges strongly to the nearest common
fixed point of the family of asymptotically nonexpansive mappings. The results presented in this paper expand and improve corresponding ones from Hilbert spaces to
uniformly convex Banach spaces, or from nonexpansive mappings to asymptotically
nonexpansive mappings.</p>