Strong convergence of the iterative methods for hierarchical fixed point problems of an infinite family of strictly nonself pseudocontractions
type: Item
instance of: scholarly article
title: Strong convergence of the iterative methods for hierarchical fixed point problems of an infinite family of strictly nonself pseudocontractions
zbMATH Open document ID: 1253.65091
DOI: 10.1155/2012/457024
author: Wei Xu
author: Yuanheng Wang
published in: Abstract and Applied Analysis
publication date: 2012-12-18T00:00:00Z
review text: Summary: We deals with a new iterative algorithm for solving hierarchical fixed point problems of an infinite family of pseudocontractions in Hilbert spaces by \(y_n = \beta_n S x_n + (1 - \beta_n)x_n, x_{n+1} = P_C[\alpha_n f(x_n) + (1 - \alpha_n) \sum^\infty_{i=1} \mu^{(n)}_i T_i y_n]\), and \(\forall n \geq 0\), where \(T_i : C \mapsto H\) is a nonself \(k_i\)-strictly pseudocontraction. Under certain approximate conditions, the sequence \(\{x_n\}\) converges strongly to \(x^\ast \in \bigcap^\infty_{i=1} F(T_i)\), which solves some variational inequality. The results here improve and extend some recent results.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 6116405
zbMATH Keywords: iterative algorithm
zbMATH Keywords: hierarchical fixed point problems
zbMATH Keywords: infinite family of pseudocontractions
zbMATH Keywords: Hilbert spaces
Wikidata QID: Q58695212
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/457024
OpenAlex ID: W2055215390
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description: scientific article; zbMATH DE number 6116405