Abstract
In this paper, we find some properties of generalized relaxed \(\eta - \alpha \) quasimonotone mappings and generalized relaxed \(\eta - \alpha \) properly quasimonotone mappings. With these generalized monotone mappings, we have proved some existence results for the variational-like inequalities. Some relations between Minty variational-like inequality problem and Stampacchia variational-like inequality problem were then established. We have also established some existence of solutions for the variational-like inequalities with densely relaxed \(\eta -\alpha \) pseudomonotone operators.
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