Iterative selection methods for common fixed point problems
type: Item
instance of: scholarly article
title: Iterative selection methods for common fixed point problems
zbMATH Open document ID: 1106.47057
author: Sever A. Hirstoaga
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-11-15T00:00:00Z
review text: The author presents two iterative methods for solving the following problem. Let \((T_n)_{n\in \mathbb{N}}\) and \((S_n)_{n\in \mathbb{N}}\) be two families of quasi-nonexpansive operators from a Hilbert space \(H\) to itself such that \(\emptyset \neq \bigcap_{n\in \mathbb{N}}\text{Fix}T_n\subset \bigcap_{n\in \mathbb{N}}\text{Fix}S_n\) and \(Q:H\rightarrow H\) be a strict contraction. Find (the unique) \(\overline{x} \in H\) such that \(\overline{x}=P_C(Q\overline{x})\), where \(P_C\) is the projection operator on \(C\). Finally, applications to monotone inclusions and equilibrium problems are considered.
reviewed by: Mircea Balaj
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 5073002
zbMATH Keywords: common fixed point
zbMATH Keywords: strict contraction
zbMATH Keywords: Hilbert space
zbMATH Keywords: convergence
zbMATH Keywords: iteration
zbMATH Keywords: quasi-nonexpansive operator
zbMATH Keywords: maximal monotone operator
zbMATH Keywords: equilibrium problem
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.12.064
OpenAlex ID: W2132614631
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DOI: 10.1016/J.JMAA.2005.12.064
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description: scientific article; zbMATH DE number 5073002