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doi:10.1016/j.na.2008.03.057 
Copyright © 2008 Elsevier Ltd All rights reserved.
Projection algorithms for solving a system of general variational inequalities
Received 7 December 2007;
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Abstract
In this paper, we introduce and consider a new system of general variational inequalities involving four different operators. Using the projection operator technique, we suggest and analyze some new explicit iterative methods for this system of variational inequalities. We also study the convergence analysis of the new iterative method under certain mild conditions. Since this new system includes the system of variational inequalities involving three operators, variational inequalities and related optimization problems as special cases, results obtained in this paper continue to hold for these problems. Our results can be viewed as a refinement and improvement of the previously known results for variational inequalities.
Keywords: General explicit iteration algorithms; System of nonlinear variational inequalities with different mappings; Relaxed (γ,r)-cocoercive mappings; Lipschitzian continuous; Hilbert spaces
Mathematical subject codes: 49J40; 90C33
