J. Korean Math. Soc. 2008; 45(3): 841-858
Printed May 1, 2008
Copyright © The Korean Mathematical Society.
Lu-Chuan Ceng, Gue Myung Lee, and Jen-Chih Yao
Shanghai Normal University, Pukyong National University, National Sun Yat-sen University
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 multifunctions 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, $\widetilde H$-hemicontinuity, coercivity
MSC numbers: 49J40, 90C29, 47H10, 47H17
1996; 33(3): 609-624
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd