GENERALIZED VARIATIONAL-LIKE INEQUALITIES WITH COMPOSITELY MONOTONE MULTIFUNCTIONS

- Journal title : Journal of the Korean Mathematical Society
- Volume 45, Issue 3, 2008, pp.841-858
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2008.45.3.841

Title & Authors

GENERALIZED VARIATIONAL-LIKE INEQUALITIES WITH COMPOSITELY MONOTONE MULTIFUNCTIONS

Ceng, Lu-Chuan; Lee, Gue-Myung; Yao, Jen-Chih;

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 monotone multifunctions in reflexive Banach spaces. On the other hand we also derive the solvability of generalized variational-like inequalities with compositely relaxed 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-hemicontinuity;coercivity;

Language

English

Cited by

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