Abstract and Applied Analysis

Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces

Genaro López, Victoria Martín-Márquez, Fenghui Wang, and Hong-Kun Xu

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 109236, 25 pages.

Dates
First available in Project Euclid: 4 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365099935

Digital Object Identifier
doi:10.1155/2012/109236

Mathematical Reviews number (MathSciNet)
MR2955015

Zentralblatt MATH identifier
1252.47043

Citation

López, Genaro; Martín-Márquez, Victoria; Wang, Fenghui; Xu, Hong-Kun. Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 109236, 25 pages. doi:10.1155/2012/109236. https://projecteuclid.org/euclid.aaa/1365099935


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