Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Published : 2008.05.31
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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.

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References

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