Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces
Joint Authors
Xu, Hong Kun
Wang, Fenghui
López, Genaro
Martín-Márquez, Victoria
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-25, 25 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-07-19
Country of Publication
Egypt
No. of Pages
25
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
López, Genaro& Martín-Márquez, Victoria& Wang, Fenghui& Xu, Hong Kun. 2012. Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-25.
https://search.emarefa.net/detail/BIM-447135
Modern Language Association (MLA)
López, Genaro…[et al.]. Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces. Abstract and Applied Analysis No. 2012 (2012), pp.1-25.
https://search.emarefa.net/detail/BIM-447135
American Medical Association (AMA)
López, Genaro& Martín-Márquez, Victoria& Wang, Fenghui& Xu, Hong Kun. Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-25.
https://search.emarefa.net/detail/BIM-447135
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-447135