On a system of general mixed variational inequalities |
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Authors: | Muhammad Aslam Noor |
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Institution: | (1) Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan |
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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. |
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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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