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http://dx.doi.org/10.4134/JKMS.2008.45.3.841

GENERALIZED VARIATIONAL-LIKE INEQUALITIES WITH COMPOSITELY MONOTONE MULTIFUNCTIONS  

Ceng, Lu-Chuan (Department of Mathematics Shanghai Normal University)
Lee, Gue-Myung (Department of Applied Mathematics Pukyong National University)
Yao, Jen-Chih (Department of Applied Mathematics National Sun Yat-Sen University)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.3, 2008 , pp. 841-858 More about this Journal
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 ${\eta}-{\alpha}$ monotone multifunctions in reflexive Banach spaces. On the other hand we also derive the solvability of generalized variational-like inequalities with compositely relaxed ${\eta}-{\alpha}$ 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$\tilde{H}$-hemicontinuity; coercivity;
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