Implicit iterative scheme for a countable family of nonexpansive mappings in 2-uniformly smooth Banach spaces (Q369825)
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scientific article; zbMATH DE number 6209236
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Implicit iterative scheme for a countable family of nonexpansive mappings in 2-uniformly smooth Banach spaces |
scientific article; zbMATH DE number 6209236 |
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Implicit iterative scheme for a countable family of nonexpansive mappings in 2-uniformly smooth Banach spaces (English)
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19 September 2013
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Summary: Implicit Mann process and Halpern-type iteration have been extensively studied by many others. In this paper, in order to find a common fixed point of a countable family of nonexpansive mappings in the framework of Banach spaces, we propose a new implicit iterative algorithm related to a strongly accretive and Lipschitzian continuous operator \(F : x_n = \alpha_n \gamma V(x_n) + \beta_n x_{n - 1} + ((1 - \beta_n)I - \alpha_n \mu F)T_n x_n\) and get strong convergence under some mild assumptions. Our results improve and extend the corresponding conclusions announced by many others.
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implicit Halpern-type iteration
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common fixed point
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countable family of nonexpansive mappings
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Banach spaces
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strong convergence
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0.9638398
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0.96117544
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0.9347325
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