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In this paper, some new classes of the strongly exponentially generalized preinvex functions involving an auxiliary non-negative function and a bifunction are introduced. New relationships among various concepts of strongly exponentially generalized preinvex functions are established. It is shown that the optimality conditions of differentiable strongly exponentially generalized preinvex functions can be characterized by exponentially variational-like inequalities. As special cases, one can obtain various new and known results from our results. Results obtained in this paper can be viewed as refinement and improvement of previously known results.