TY - JOUR
T1 - Weak Convergence Theorems for Nonself Mappings
AU - Liu , Yongquan
AU - Guo , Weiping
JO - Communications in Mathematical Research 
VL - 1
SP - 15
EP - 22
PY - 2021
DA - 2021/05
SN - 31
DO - http://doi.org/10.13447/j.1674-5647.2015.01.02
UR - https://global-sci.org/intro/article_detail/cmr/18945.html
KW - asymptotically nonexpansive nonself-mapping, weak convergence, uniformly convex Banach space, common fixed point, smooth Banach space.
AB - <p style="text-align: justify;">Let $E$ be a real uniformly convex and smooth Banach space, and $K$ be a nonempty closed convex subset of $E$ with $P$ as a sunny nonexpansive retraction. Let $T_1, T_2 : K → E$ be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with a sequence $\{k^{(i)}_n\} ⊂ [1, ∞) (i = 1, 2)$, and $F := F(T_1)
∩
F(T_2)&nbsp;≠&nbsp;∅$. An iterative sequence for approximation common fixed
points of the two nonself asymptotically nonexpansive mappings is discussed. If $E$ also has a Fréchet differentiable norm or its dual $E^∗$ has Kadec-Klee property, then
weak convergence theorems are obtained.</p>