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Hybrid and Relaxed Mann Iterations for General Systems of Variational Inequalities and Nonexpansive Mappings
Joint Authors
Latif, Abdul
al-Mazrooei, Abdullah E.
Ceng, Lu-Chuan
Abdou, A. A. N.
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-44, 44 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-28
Country of Publication
Egypt
No. of Pages
44
Main Subjects
Abstract EN
We introduce hybrid and relaxed Mann iteration methods for a general system of variational inequalities with solutions being also common solutions of a countable family of variational inequalities and common fixed points of a countable family of nonexpansive mappings in real smooth and uniformly convex Banach spaces.
Here, the hybrid and relaxed Mann iteration methods are based on Korpelevich’s extragradient method, viscosity approximation method, and Mann iteration method.
Under suitable assumptions, we derive some strong convergence theorems for hybrid and relaxed Mann iteration algorithms not only in the setting of uniformly convex and 2-uniformly smooth Banach space but also in a uniformly convex Banach space having a uniformly Gateaux differentiable norm.
The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.
American Psychological Association (APA)
Ceng, Lu-Chuan& al-Mazrooei, Abdullah E.& Abdou, A. A. N.& Latif, Abdul. 2013. Hybrid and Relaxed Mann Iterations for General Systems of Variational Inequalities and Nonexpansive Mappings. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-44.
https://search.emarefa.net/detail/BIM-446508
Modern Language Association (MLA)
Ceng, Lu-Chuan…[et al.]. Hybrid and Relaxed Mann Iterations for General Systems of Variational Inequalities and Nonexpansive Mappings. Abstract and Applied Analysis No. 2013 (2013), pp.1-44.
https://search.emarefa.net/detail/BIM-446508
American Medical Association (AMA)
Ceng, Lu-Chuan& al-Mazrooei, Abdullah E.& Abdou, A. A. N.& Latif, Abdul. Hybrid and Relaxed Mann Iterations for General Systems of Variational Inequalities and Nonexpansive Mappings. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-44.
https://search.emarefa.net/detail/BIM-446508
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-446508