Generalized extragradient iterative method for systems of variational inequalities
1 Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2 Scientific Computing Key Laboratory of Shanghai Universities, Chung Li 32023, Taiwan Shanghai, China
3 Department of Applied Mathematics, Chung Yuan Christian University, Chung Li 32023, Taiwan
4 Department of Mathematics, King Abdulaziz University, P.O.Box 80203, Jeddah 21589, Saudi Arabia
Journal of Inequalities and Applications 2012, 2012:88 doi:10.1186/1029-242X-2012-88Published: 16 April 2012
The purpose of this article is to investigate the problem of finding a common element of the solution sets of two different systems of variational inequalities and the set of fixed points a strict pseudocontraction mapping defined in the setting of a real Hilbert space. Based on the well-known extragradient method, viscosity approximation method and Mann iterative method, we propose and analyze a generalized extra-gradient iterative method for computing a common element. Under very mild assumptions, we obtain a strong convergence theorem for three sequences generated by the proposed method. Our proposed method is quite general and flexible and includes the iterative methods considered in the earlier and recent literature as special cases. Our result represents the modification, supplement, extension and improvement of some corresponding results in the references.
Mathematics Subject Classification (2000): Primary 49J40; Secondary 65K05; 47H09.