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2012 Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces
Genaro López, Victoria Martín-Márquez, Fenghui Wang, Hong-Kun Xu
Abstr. Appl. Anal. 2012(SI11): 1-25 (2012). DOI: 10.1155/2012/109236


Splitting methods have recently received much attention due to the fact that many nonlinear problems arising in applied areas such as image recovery, signal processing, and machine learning are mathematically modeled as a nonlinear operator equation and this operator is decomposed as the sum of two (possibly simpler) nonlinear operators. Most of the investigation on splitting methods is however carried out in the framework of Hilbert spaces. In this paper, we consider these methods in the setting of Banach spaces. We shall introduce two iterative forward-backward splitting methods with relaxations and errors to find zeros of the sum of two accretive operators in the Banach spaces. We shall prove the weak and strong convergence of these methods under mild conditions. We also discuss applications of these methods to variational inequalities, the split feasibility problem, and a constrained convex minimization problem.


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Genaro López. Victoria Martín-Márquez. Fenghui Wang. Hong-Kun Xu. "Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces." Abstr. Appl. Anal. 2012 (SI11) 1 - 25, 2012.


Published: 2012
First available in Project Euclid: 4 April 2013

zbMATH: 1252.47043
MathSciNet: MR2955015
Digital Object Identifier: 10.1155/2012/109236

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI11 • 2012
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