Strong convergence theorems by an extragradient method for solving variational inequalities and equilibrium problems in a Hilbert space
Journal article
Authors/Editors
Strategic Research Themes
No matching items found.
Publication Details
Author list: Kumam P.
Publication year: 2009
Journal: Turkish Journal of Mathematics (1300-0098)
Volume number: 33
Issue number: 1
Start page: 85
End page: 98
Number of pages: 14
ISSN: 1300-0098
Languages: English-Great Britain (EN-GB)
View in Web of Science | View on publisher site | View citing articles in Web of Science
Abstract
In this paper, we introduce an iterative process for finding the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for monotone, Lipschitz-continuous mappings. The iterative process is based on the so-called extragradient method. We show that the sequence converges strongly to a common element of the above three sets under some parametric controlling conditions. This main theorem extends a recent result of Yao, Liou and Yao [Y. Yao, Y. C. Liou and J.-C. Yao, "An Extragradient Method for Fixed Point Problems and Variational Inequality Problems," Journal of Inequalities and Applications Volume 2007, Article ID 38752, 12 pages doi:10.1155/2007/38752] and many others. © TÜBİTAK.
Keywords
Lipschitz-continuous mappings
Contact Information