Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces
We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let C be a bounded closed convex subset of a uniformly smooth Banach space E. Let {Tn:n∈ℕ} be an infinite family of commuting nonexpansive mapp...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2006-06-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/FPTA/2006/59692 |
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doaj-a028e1ca7c0445d3b0b30d3372a4c5372020-11-24T23:27:18ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122006-06-01200610.1155/FPTA/2006/59692Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spacesTomonari SuzukiWe prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let C be a bounded closed convex subset of a uniformly smooth Banach space E. Let {Tn:n∈ℕ} be an infinite family of commuting nonexpansive mappings on C. Let {αn} and {tn} be sequences in (0,1/2) satisfying limntn=limnαn/tnℓ=0 for ℓ∈ℕ. Fix u∈C and define a sequence {un} in C by un=(1−αn)((1−∑k=1ntnk)T1un+∑k=1ntnkTk+1un)+αnu for n∈ℕ. Then {un} converges strongly to Pu, where P is the unique sunny nonexpansive retraction from C onto ∩n=1∞F(Tn).http://dx.doi.org/10.1155/FPTA/2006/59692 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Tomonari Suzuki |
| spellingShingle |
Tomonari Suzuki Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces Fixed Point Theory and Applications |
| author_facet |
Tomonari Suzuki |
| author_sort |
Tomonari Suzuki |
| title |
Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces |
| title_short |
Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces |
| title_full |
Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces |
| title_fullStr |
Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces |
| title_full_unstemmed |
Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces |
| title_sort |
browder's type strong convergence theorems for infinite families of nonexpansive mappings in banach spaces |
| publisher |
SpringerOpen |
| series |
Fixed Point Theory and Applications |
| issn |
1687-1820 1687-1812 |
| publishDate |
2006-06-01 |
| description |
We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let C be a bounded closed convex subset of a uniformly smooth Banach space E. Let {Tn:n∈ℕ} be an infinite family of commuting nonexpansive mappings on C. Let {αn} and {tn} be sequences in (0,1/2) satisfying limntn=limnαn/tnℓ=0 for ℓ∈ℕ. Fix u∈C and define a sequence {un} in C by un=(1−αn)((1−∑k=1ntnk)T1un+∑k=1ntnkTk+1un)+αnu for n∈ℕ. Then {un} converges strongly to Pu, where P is the unique sunny nonexpansive retraction from C onto ∩n=1∞F(Tn). |
| url |
http://dx.doi.org/10.1155/FPTA/2006/59692 |
| work_keys_str_mv |
AT tomonarisuzuki browderstypestrongconvergencetheoremsforinfinitefamiliesofnonexpansivemappingsinbanachspaces |
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1716315638036692992 |