Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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GENERALIZED SET-VALVED STRONGLY NONLINEAR VARIATIONAL INEQUALITIES IN BANACH SPACES

  • Cho, Y.J. (Department of Mathematics Gyeongsan national University) ;
  • Fang, Y.P. (Department of Mathemetics Sichuan University) ;
  • Huang, N.J. (Department of Mathemetics Sichuan University) ;
  • Kim, K.H. (Department of Mathematics Gyeongsan national University)
  • Published : 2003.03.01
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Abstract

In this paper, we introduce and study a new class of generalized strongly nonlinear variational inequalities with setvalued mappings. By using the KKM technique, we prove the existence and uniqueness of solution for this class of generalized setvalued strongly nonlinear variational inequalities in reflexive Banach spaces. Our results include the main results of Verma ［16］, ［17］ as special cases.

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References

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  1. On the Index of Solvability for Variational Inequalities in Banach Spaces vol.16, pp.1, 2008, https://doi.org/10.1007/s11228-007-0046-8
  2. The penalty method for generalized multivalued nonlinear variational inequalities in Banach spaces vol.20, pp.8, 2007, https://doi.org/10.1016/j.aml.2006.11.002