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Implicit Relaxed and Hybrid Methods with Regularization for Minimization Problems and Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense
Joint Authors
Ceng, Lu-Chuan
Wen, Ching-Feng
Ansari, Qamrul Hasan
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-04-16
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
We first introduce an implicit relaxed method with regularization for finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping S in the intermediate sense and the set of solutions of the minimization problem (MP) for a convex and continuously Frechet differentiable functional in the setting of Hilbert spaces.
The implicit relaxed method with regularization is based on three well-known methods: the extragradient method, viscosity approximation method, and gradient projection algorithm with regularization.
We derive a weak convergence theorem for two sequences generated by this method.
On the other hand, we also prove a new strong convergence theorem by an implicit hybrid method with regularization for the MP and the mapping S.
The implicit hybrid method with regularization is based on four well-known methods: the CQ method, extragradient method, viscosity approximation method, and gradient projection algorithm with regularization.
American Psychological Association (APA)
Ceng, Lu-Chuan& Ansari, Qamrul Hasan& Wen, Ching-Feng. 2013. Implicit Relaxed and Hybrid Methods with Regularization for Minimization Problems and Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-14.
https://search.emarefa.net/detail/BIM-503602
Modern Language Association (MLA)
Ceng, Lu-Chuan…[et al.]. Implicit Relaxed and Hybrid Methods with Regularization for Minimization Problems and Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense. Abstract and Applied Analysis No. 2013 (2013), pp.1-14.
https://search.emarefa.net/detail/BIM-503602
American Medical Association (AMA)
Ceng, Lu-Chuan& Ansari, Qamrul Hasan& Wen, Ching-Feng. Implicit Relaxed and Hybrid Methods with Regularization for Minimization Problems and Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-14.
https://search.emarefa.net/detail/BIM-503602
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-503602