A Viscosity Hybrid Steepest Descent Method for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems of Infinite Family of Strictly Pseudocontractive Mappings and Nonexpansive Semigroup
Joint Authors
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-24, 24 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-07-30
Country of Publication
Egypt
No. of Pages
24
Main Subjects
Abstract EN
In this paper, modifying the set of variational inequality and extending the nonexpansive mapping of hybrid steepest descent method to nonexpansive semigroups, we introduce a new iterative scheme by using the viscosity hybrid steepest descent method for finding a common element of the set of solutions of a system of equilibrium problems, the set of fixed points of an infinite family of strictly pseudocontractive mappings, the set of solutions of fixed points for nonexpansive semigroups, and the sets of solutions of variational inequality problems with relaxed cocoercive mapping in a real Hilbert space.
We prove that the sequence converges strongly to a common element of the above sets under some mild conditions.
The results shown in this paper improve and extend the recent ones announced by many others.
American Psychological Association (APA)
Che, Haitao& Pan, Xintian. 2013. A Viscosity Hybrid Steepest Descent Method for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems of Infinite Family of Strictly Pseudocontractive Mappings and Nonexpansive Semigroup. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-24.
https://search.emarefa.net/detail/BIM-454298
Modern Language Association (MLA)
Che, Haitao& Pan, Xintian. A Viscosity Hybrid Steepest Descent Method for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems of Infinite Family of Strictly Pseudocontractive Mappings and Nonexpansive Semigroup. Abstract and Applied Analysis No. 2013 (2013), pp.1-24.
https://search.emarefa.net/detail/BIM-454298
American Medical Association (AMA)
Che, Haitao& Pan, Xintian. A Viscosity Hybrid Steepest Descent Method for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems of Infinite Family of Strictly Pseudocontractive Mappings and Nonexpansive Semigroup. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-24.
https://search.emarefa.net/detail/BIM-454298
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-454298