Weak convergence theorems for asymptotically nonexpansive nonself-mappings

作者：Guo, Weiping^*; Guo, Wei

来源：Applied Mathematics Letters, 2011, 24(12): 2181-2185.

DOI：10.1016/j.aml.2011.06.022

• Asymptotically nonexpansive nonself-mapping
• Weak convergence
• Common fixed point
• Uniformly convex Banach space

Suppose that K is a nonempty closed convex subset of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T-1, T-2 : K -> E be two asymptotically nonexpansive nonself-mappings with sequences {k(n)}, {l(n)} subset of |1, infinity| such that Sigma(infinity)(n=1)(k(n) - 1) < infinity and Sigma(infinity)(n=1)(l(n) - 1) < infinity, respectively and F(T-1)boolean AND F(T-2) = {x is an element of K : T(1)x = T(2)x = x} not equal empty set. Suppose that {x(n)} is generated iteratively by
{ x(1) is an element of K
x(n+1) = P((1 - alpha(n))x(n) + alpha T-n(1) (PT1)(n-1)y(n))
y(n) = P((1 - beta(n))x(n) + beta T-n(2)(PT2)(n-1)x(n)), for all n >= 1.
where {alpha(n)} and {beta(n)} are two real sequences in |epsilon, 1 - epsilon| for some epsilon > 0. If E also has a Trechet differentiable norm or its dual E* has the Kadec-Klee property, then weak convergence of {x(n)} to some q is an element of F(T-1) boolean AND F(T-2) are obtained.

• 出版日期2011-12
• 单位苏州科技大学