A Class of Variational-Like Inequalities in Banach Spaces: Variational-Like Inequalities

Abstract

In 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.