Generalized Variational-like Inequalities with Compositely Monotone Multifunctions
نویسندگان
چکیده
In this paper, we introduce two classes of generalized variational-like inequalities with compositely monotone multifunctions in Banach spaces. Using the KKM-Fan lemma and the Nadler’s result, we prove the existence of solutions for generalized variational-like inequalities with compositely relaxed η − α monotone multifunctions in reflexive Banach spaces. On the other hand we also derive the solvability of generalized variational-like inequalities with compositely relaxed η−α semimonotone multifunctions in arbitrary Banach spaces by virtue of the Kakutani-FanGlicksberg fixed-point theorem. The results presented in this paper extend and improve some earlier and recent results in the literature.
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