A Viscosity Hybrid Steepest Descent Method for Generalized Mixed Equilibrium Problems and Variational Inequalities for Relaxed Cocoercive Mapping in Hilbert Spaces
Joint Authors
Kumam, Poom
Jaiboon, Chaichana
Chantarangsi, Wanpen
Source
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-39, 39 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-07-20
Country of Publication
Egypt
No. of Pages
39
Main Subjects
Abstract EN
We present an iterative method for fixed point problems, generalized mixed equilibrium problems, and variational inequality problems.
Our method is based on the so-called viscosity hybrid steepest descent method.
Using this method, we can find the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of generalized mixed equilibrium problems, and the set of solutions of variational inequality problems for a relaxed cocoercive mapping in a real Hilbert space.
Then, we prove the strong convergence of the proposed iterative scheme to the unique solution of variational inequality.
The results presented in this paper generalize and extend some well-known strong convergence theorems in the literature.
American Psychological Association (APA)
Chantarangsi, Wanpen& Jaiboon, Chaichana& Kumam, Poom. 2010. A Viscosity Hybrid Steepest Descent Method for Generalized Mixed Equilibrium Problems and Variational Inequalities for Relaxed Cocoercive Mapping in Hilbert Spaces. Abstract and Applied Analysis،Vol. 2010, no. 2010, pp.1-39.
https://search.emarefa.net/detail/BIM-468382
Modern Language Association (MLA)
Chantarangsi, Wanpen…[et al.]. A Viscosity Hybrid Steepest Descent Method for Generalized Mixed Equilibrium Problems and Variational Inequalities for Relaxed Cocoercive Mapping in Hilbert Spaces. Abstract and Applied Analysis No. 2010 (2010), pp.1-39.
https://search.emarefa.net/detail/BIM-468382
American Medical Association (AMA)
Chantarangsi, Wanpen& Jaiboon, Chaichana& Kumam, Poom. A Viscosity Hybrid Steepest Descent Method for Generalized Mixed Equilibrium Problems and Variational Inequalities for Relaxed Cocoercive Mapping in Hilbert Spaces. Abstract and Applied Analysis. 2010. Vol. 2010, no. 2010, pp.1-39.
https://search.emarefa.net/detail/BIM-468382
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-468382