On iterative methods for solving a system of mixed variational inequalities

Abstract

In this article, we introduce and consider a new system of mixed variational inequalities involving two different operators. Using the resolvent operator technique, we suggest and analyse some new explicit iterative methods for this system of 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 variational inequalities involving the single operator, variational inequalities and related optimization problems as special cases, results obtained in this article 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

AMS 2000 Subject Classifications: :

• 49J40
• 90C33

Acknowledgements

The author would like to thank Dr S.M. Junaid Zaidi, Rector, CIIT, for providing excellent research facilities and the referees for their very useful and constructive comments.