GENERALIZED VARIATIONAL-LIKE INEQUALITIES WITH COMPOSITELY MONOTONE MULTIFUNCTIONS

Title & Authors
GENERALIZED VARIATIONAL-LIKE INEQUALITIES WITH COMPOSITELY MONOTONE MULTIFUNCTIONS
Ceng, Lu-Chuan; Lee, Gue-Myung; Yao, Jen-Chih;

Abstract
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 $\small{{\eta}-{\alpha}}$ monotone multifunctions in reflexive Banach spaces. On the other hand we also derive the solvability of generalized variational-like inequalities with compositely relaxed $\small{{\eta}-{\alpha}}$ semimonotone multi functions in arbitrary Banach spaces by virtue of the Kakutani-Fan-Glicksberg fixed-point theorem. The results presented in this paper extend and improve some earlier and recent results in the literature.
Keywords
generalized variational-like inequalities;compositely (semi) monotone multifunctions;KKM mappings;Hausdorff metric$\small{\tilde{H}}$-hemicontinuity;coercivity;
Language
English
Cited by
1.
Existence theorems for relaxed η-α pseudomonotone and strictly η-quasimonotone generalized variational-like inequalities, Journal of Inequalities and Applications, 2014, 2014, 1, 442
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