Optimization Letters

, Volume 3, Issue 3, pp 437–451 | Cite as

On a system of general mixed variational inequalities

Original Paper
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Abstract

In this paper, we introduce and consider a new system of general mixed variational inequalities involving three different operators. Using the resolvent operator technique, we establish the equivalence between the general mixed variational inequalities and the fixed point problems. We use this equivalent formulation to suggest and analyze some new explicit iterative methods for this system of general mixed 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 mixed variational inequalities involving two 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 general variational inequalities with different mappings Relaxed (γ, r)-cocoercive mappings Lipschitzian continuous Hilbert spaces 
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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Mathematics DepartmentCOMSATS Institute of Information TechnologyIslamabadPakistan

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