[HTML][HTML] Weak convergence theorems for asymptotically nonexpansive nonself-mappings
W Guo, W Guo - Applied mathematics letters, 2011 - Elsevier
W Guo, W Guo
Applied mathematics letters, 2011•ElsevierSuppose that K is a nonempty closed convex subset of a real uniformly convex Banach
space E with P as a nonexpansive retraction. Let T1, T2: K→ E be two asymptotically
nonexpansive nonself-mappings with sequences {kn},{ln}⊂[1,∞) such that∑ n= 1∞(kn−
1)<∞ and∑ n= 1∞(ln− 1)<∞, respectively and F (T1)∩ F (T2)={x∈ K: T1x= T2x= x}≠ 0̸.
Suppose that {xn} is generated iteratively by where {αn} and {βn} are two real sequences in
[ϵ, 1− ϵ] for some ϵ> 0. If E also has a Fréchet differentiable norm or its dual E∗ has the …
space E with P as a nonexpansive retraction. Let T1, T2: K→ E be two asymptotically
nonexpansive nonself-mappings with sequences {kn},{ln}⊂[1,∞) such that∑ n= 1∞(kn−
1)<∞ and∑ n= 1∞(ln− 1)<∞, respectively and F (T1)∩ F (T2)={x∈ K: T1x= T2x= x}≠ 0̸.
Suppose that {xn} is generated iteratively by where {αn} and {βn} are two real sequences in
[ϵ, 1− ϵ] for some ϵ> 0. If E also has a Fréchet differentiable norm or its dual E∗ has the …
Suppose that K is a nonempty closed convex subset of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T1,T2:K→E be two asymptotically nonexpansive nonself-mappings with sequences {kn},{ln}⊂[1,∞) such that ∑n=1∞(kn−1)<∞ and ∑n=1∞(ln−1)<∞, respectively and F(T1)∩F(T2)={x∈K:T1x=T2x=x}≠0̸. Suppose that {xn} is generated iteratively by where {αn} and {βn} are two real sequences in [ϵ,1−ϵ] for some ϵ>0. If E also has a Fréchet differentiable norm or its dual E∗ has the Kadec–Klee property, then weak convergence of {xn} to some q∈F(T1)∩F(T2) are obtained.
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