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arXiv · 0712.1172

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

Jean-Philippe Chancelier
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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 $J_Φ$ with gauge $ϕ$. Let $f$ be an {\em $α$-contraction} and $\{T_n\}$ a sequence of nonexpansive mapping, we study the strong convergence of explicit iterative schemes x_{n+1} = α_n f(x_n) + (1-α_n) T_n x_n with a general theorem and then recover and improve some specific cases studied in the literature

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Jean-Philippe Chancelier. 2007-12-07. Iterative schemes for computing fixed points of nonexpansive mappings in Banach spaces. https://arxiv.org/abs/0712.1172

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