In this paper, we investigate the existence of solutions for generalized variational-like inequalities (for short GVLI). In reflexive Banach spaces, when the constraint set is bounded, we deduce an existence theorem for GVLI. In finite dimensional spaces, employing this result, when the constraint set is unbounded, we obtain an existence theorem for GVLI, where the mapping and the constraint set are simultaneously perturbed, which generalizes some recent results in this topic. Moreover, we show that there is a solution of GVLI in Kr under the same coercivity condition.
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