Mohapatra R.N.; Sahu B.K.; Pani S.2025-02-1720211http://dx.doi.org/10.1007/978-981-33-4646-8_47https://idr.iitbbs.ac.in/handle/2008/3682In this paper, we find some properties of generalized relaxed ?- ? quasimonotone mappings and generalized relaxed ?- ? 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 ?- ? pseudomonotone operators. � 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.enDensely relaxed ?- ? pseudomonotone operators; Generalized relaxed ?- ? properly quasimonotonicity; Generalized relaxed ?- ? quasimonotonicity; KKM mapping; Variational-like inequalitiesConference paper