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Mann-Type Viscosity Approximation Methods for Multivalued Variational Inclusions with Finitely Many Variational Inequality Constraints in Banach Spaces
Joint Authors
Latif, Abdul
al-Mazrooei, Abdullah E.
Ceng, Lu-Chuan
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-12-05
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
We introduce Mann-type viscosity approximation methods for finding solutions of a multivalued variational inclusion (MVVI) which are also common ones of finitely many variational inequality problems and common fixed points of a countable family of nonexpansive mappings in real smooth Banach spaces.
Here the Mann-type viscosity approximation methods are based on the Mann iteration method and viscosity approximation method.
We consider and analyze Mann-type viscosity iterative 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 Gáteaux differentiable norm.
Under suitable assumptions, we derive some strong convergence theorems.
In addition, we also give some applications of these theorems; for instance, we prove strong convergence theorems for finding a common fixed point of a finite family of strictly pseudocontractive mappings and a countable family of nonexpansive mappings in uniformly convex and 2-uniformly smooth Banach spaces.
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& Latif, Abdul& al-Mazrooei, Abdullah E.. 2013. Mann-Type Viscosity Approximation Methods for Multivalued Variational Inclusions with Finitely Many Variational Inequality Constraints in Banach Spaces. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-18.
https://search.emarefa.net/detail/BIM-463949
Modern Language Association (MLA)
Ceng, Lu-Chuan…[et al.]. Mann-Type Viscosity Approximation Methods for Multivalued Variational Inclusions with Finitely Many Variational Inequality Constraints in Banach Spaces. Abstract and Applied Analysis No. 2013 (2013), pp.1-18.
https://search.emarefa.net/detail/BIM-463949
American Medical Association (AMA)
Ceng, Lu-Chuan& Latif, Abdul& al-Mazrooei, Abdullah E.. Mann-Type Viscosity Approximation Methods for Multivalued Variational Inclusions with Finitely Many Variational Inequality Constraints in Banach Spaces. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-18.
https://search.emarefa.net/detail/BIM-463949
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-463949