Strong convergence theorems for strict pseudo-contractions in \(q\)-uniformly smooth Banach spaces
type: Item
instance of: scholarly article
title: Strong convergence theorems for strict pseudo-contractions in \(q\)-uniformly smooth Banach spaces
zbMATH Open document ID: 1177.47085
author: Hong Zhang
author: Yongfu Su
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-04-02T00:00:00Z
review text: Let \(C\) be a closed convex subset of a real \(q\)-uniformly smooth Banach space and \(T_i:C\to C\), \(i=1,2,\dots,N\), be a finite family of mappings which are strictly pseudo-contractive. Assume that \(F:= \bigcap^N_{i=1}F(T_i)\neq\emptyset\). Let \(u,x_0\in C\) be arbitrary fixed vectors in \(C\). It is proved that the sequence \(\{x_n\}_{n\geq 0}\) generated by \[ \begin{cases} y_n=(1-\alpha_n)x_n+\alpha_n \sum^N_{i=1} \eta_i^{(n)}T_ix_n,\\ x_{n+1}=\beta_nu+\gamma_nx_n+\delta_ny_n, \end{cases} \] where \(\{\alpha_n\}\), \(\{\beta_n\}\), \(\{\gamma_n\}\) and \(\{\sigma_n\}\) are sequences in \((0,1)\) satisfying appropriate conditions, converges strongly to an element of \(F\).
reviewed by: Jürgen Appell
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 5539203
zbMATH Keywords: strong convergence
zbMATH Keywords: \(\lambda\)-strict pseudocontraction
zbMATH Keywords: normal Mann iteration
zbMATH Keywords: parallel algorithm
zbMATH Keywords: \(q\)-uniformly smooth Banach spaces
MaRDI profile type: Publication
full work available at URL: j.na.2008.04.030
OpenAlex ID: W4247579199
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DOI: 10.1016/J.NA.2008.04.030
description: scientific article; zbMATH DE number 5539203