The aim of this work is to study a system of generalized mixed variational inequalities, existence and approximation of its solution using the resolvent operator technique. We further propose an algorithm which converges to its solution and common fixed points of two Lipschitzian mappings. Parallel algorithms are used, which can be used to simultaneous computation in multiprocessor computers. The results presented in this work are more general and include many previously known results as special cases.
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