Solving split common fixed-point problem of firmly quasi-nonexpansive mappings without prior knowledge of operators norms
type: Item
instance of: scholarly article
title: Solving split common fixed-point problem of firmly quasi-nonexpansive mappings without prior knowledge of operators norms
zbMATH Open document ID: 1472.47098
DOI: 10.1155/2014/389689
author: Jing Zhao
author: Hang Zhang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Very recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms for the split common fixed-point problem concerned two bounded linear operators [\textit{A. Moudafi}, J. Nonlinear Convex Anal. 15, No. 4, 809--818 (2014; Zbl 1393.47034)]. However, to employ Moudafi's algorithms, one needs to know a prior norm (or at least an estimate of the norm) of the bounded linear operators. To estimate the norm of an operator is very difficult, if it is not an impossible task. It is the purpose of this paper to introduce a viscosity iterative algorithm with a way of selecting the stepsizes such that the implementation of the algorithm does not need any prior information about the operator norms. We prove the strong convergence of the proposed algorithms for split common fixed-point problem governed by the firmly quasi-nonexpansive operators. As a consequence, we obtain strong convergence theorems for split feasibility problem and split common null point problems of maximal monotone operators. Our results improve and extend the corresponding results announced by many others.
Mathematics Subject Classification ID: 47J26
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 7022287
zbMATH Keywords: norm estimate
zbMATH Keywords: viscosity iterative algorithm
zbMATH Keywords: strong convergence
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/389689
OpenAlex ID: W2114271968
Wikidata QID: Q59037139
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description: scientific article; zbMATH DE number 7022287