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Weak convergence theorems for asymptotically nonexpansive nonself-mappings

✍ Scribed by Weiping Guo; Wei Guo

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
221 KB
Volume
24
Category
Article
ISSN
0893-9659

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✦ Synopsis

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 β†’ E be two asymptotically nonexpansive nonself-mappings with sequences

where {α n } and {β n } are two real sequences in [ϡ, 1 -ϡ] for some ϡ > 0. If E also has a Fréchet differentiable norm or its dual E * has the Kadec-Klee property, then weak convergence of {x n } to some q ∈ F (T 1 ) ∩ F (T 2 ) are obtained.

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