Abstract
In this paper. we introduce and study a new class of variational inequalities which is called the general strongly nonlinear mixed variational-like inequalities. This class is the most general and unifying one , The auxiliary principle technique is used to prove the unique existence of a solution of the variational-like inequality and to suggest a novel and innovative iterative algorithm. We also study the convergence analysis of the iterative algorithm. Several special cases. which can be obtained from our main results, are also discussed
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