# Iterative schemes for computing fixed points of nonexpansive mappings in Banach spaces

Abstract : Let $X$ be a real Banach space with a normalized duality mapping uniformly norm-to-weak$^\star$ continuous on bounded sets or a reflexive Banach space which admits a weakly continuous duality mapping $J_{\Phi}$ with gauge $\phi$. Let $f$ be an {\em $\alpha$-contraction} and $\{T_n\}$ a sequence of nonexpansive mapping, we study the strong convergence of explicit iterative schemes $$x_{n+1} = \alpha_n f(x_n) + (1-\alpha_n) T_n x_n$$ with a general theorem and then recover and improve some specific cases studied in the literature
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-00184662
Contributor : Jean-Philippe Chancelier <>
Submitted on : Friday, December 7, 2007 - 4:48:16 PM
Last modification on : Friday, November 29, 2019 - 12:14:23 PM
Long-term archiving on: : Thursday, September 23, 2010 - 4:52:45 PM

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non-exp-map-3.pdf
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### Identifiers

• HAL Id : hal-00184662, version 3
• ARXIV : 0712.1172

### Citation

Jean-Philippe Chancelier. Iterative schemes for computing fixed points of nonexpansive mappings in Banach spaces. 2007. ⟨hal-00184662v3⟩

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