Iterative Algorithms Approach to Variational Inequalities and Fixed Point Problems

Yeong-Cheng Liou, Yonghong Yao, Chun-Wei Tseng, Hui-To Lin and Pei-Xia Yang

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: 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.

Date: 2012
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2012/949141

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:949141

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().