Pointwise Lipschitzian mappings in uniformly convex and uniformly smooth Banach spaces (Q388470)
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scientific article; zbMATH DE number 6239811
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pointwise Lipschitzian mappings in uniformly convex and uniformly smooth Banach spaces |
scientific article; zbMATH DE number 6239811 |
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Pointwise Lipschitzian mappings in uniformly convex and uniformly smooth Banach spaces (English)
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19 December 2013
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fixed point
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asymptotic pointwise nonexpansive map
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fixed point iteration process
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Mann iteration process
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Ishikawa iteration process
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weak convergence
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uniformly convex Banach space
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uniformly smooth Banach space
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Fréchet differentiable norm
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0.93866134
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0.9348629
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0.9336738
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0.93300086
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0.93276596
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0.9246345
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Let \(C\) be a bounded, closed and convex subset of a uniformly convex and uniformly smooth Banach space. Using some typical assumptions, the author shows that the generalized Mann and Ishikawa iterations converge weakly to a fixed point of an asymptotic pointwise nonexpansive map \(T\) from \(C\) to itself.NEWLINENEWLINEThroughout the paper, Banach spaces are not assumed to possess the Opial property.
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