In this paper, we suggest and analyze some new implicit methods for solving the variational inequalities. These new methods include the extra gradient method of Korpelevich (1976) and the modified extra gradient method of Noor (2004, 2010) as special cases. We also consider the convergence of this new implicit iterative method under some conditions. The ideas and techniques of this paper may stimulate further research in this dynamic area of pure and applied sciences.
Key words: Variational inequality, implicit iterative method, convergence.
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