Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities

Lu-Chuan Ceng (), Chang-yu Wang and Jen-Chih Yao ()

Mathematical Methods of Operations Research, 2008, vol. 67, issue 3, 375-390

Abstract: In this paper, we introduce and study a relaxed extragradient method for finding solutions of a general system of variational inequalities with inverse-strongly monotone mappings in a real Hilbert space. First, this system of variational inequalities is proven to be equivalent to a fixed point problem of nonexpansive mapping. Second, by using the demi-closedness principle for nonexpansive mappings, we prove that under quite mild conditions the iterative sequence defined by the relaxed extragradient method converges strongly to a solution of this system of variational inequalities. In addition, utilizing this result, we provide some applications of the considered problem not just giving a pure extension of existing mathematical problems. Copyright Springer-Verlag 2008

Keywords: Nonexpansive mapping; Common fixed point; Demi-closedness principle; Inverse-strongly monotone mapping; General system of variational inequalities; 49J30; 49J40; 47H05; 47H10 (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (17)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00186-007-0207-4 (text/html)
Access to full text is restricted to subscribers.

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:spr:mathme:v:67:y:2008:i:3:p:375-390

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-007-0207-4

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().