![](/images/graphics-bg.png)
Iterative Algorithms Approach to Variational Inequalities and Fixed Point Problems
Joint Authors
Lin, Hui-To
Yang, Pei-Xia
Liou, Yeong-Cheng
Tseng, Chun-Wei
Yao, Yonghong
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-01-16
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
We consider a general variational inequality and fixed point problem, which is to find a point x* with the property that (GVF): x*∈GVI(C,A) and g(x*)∈Fix(S) where GVI(C,A) is the solution set of some variational inequality Fix(S) is the fixed points set of nonexpansive mapping S, and g is a nonlinear operator.
Assume the solution set Ω of (GVF) is nonempty.
For solving (GVF), we suggest the following method g(xn+1)=βg(xn)+(1-β)SPC[αnF(xn)+(1-αn)(g(xn)-λAxn)], n≥0.
It is shown that the sequence {xn} converges strongly to x*∈Ω which is the unique solution of the variational inequality 〈F(x*)-g(x*),g(x)-g(x*)〉≤0, for all x∈Ω.
American Psychological Association (APA)
Liou, Yeong-Cheng& Yao, Yonghong& Tseng, Chun-Wei& Lin, Hui-To& Yang, Pei-Xia. 2012. Iterative Algorithms Approach to Variational Inequalities and Fixed Point Problems. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-15.
https://search.emarefa.net/detail/BIM-510635
Modern Language Association (MLA)
Liou, Yeong-Cheng…[et al.]. Iterative Algorithms Approach to Variational Inequalities and Fixed Point Problems. Abstract and Applied Analysis No. 2012 (2012), pp.1-15.
https://search.emarefa.net/detail/BIM-510635
American Medical Association (AMA)
Liou, Yeong-Cheng& Yao, Yonghong& Tseng, Chun-Wei& Lin, Hui-To& Yang, Pei-Xia. Iterative Algorithms Approach to Variational Inequalities and Fixed Point Problems. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-15.
https://search.emarefa.net/detail/BIM-510635
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-510635