• Cho, Y.J. ;
  • Fang, Y.P. ;
  • Huang, N.J. ;
  • Kim, K.H.
  • Published : 2003.03.01


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.


strongly nonlinear variational inequality;set valued-mapping;generalized monotone type mapping;generalized Lipschitzian type mapping;the KKm mapping


  1. Appl. Math. Lett. v.13 no.6 Sensitivity analysis for strongly nonlinear quasi-variational inclusions R. P. Agarwal;Y. J. Cho;N. J. Huang
  2. Z. Angew. Math. Mech. v.79 Generalized nonlinear implicit quasi-variational inclusion and an application to implicit variational inequalities N. J. Huang<569::AID-ZAMM569>3.0.CO;2-G
  3. Computers Math. Appl. v.40 no.2-3 Generalized nonlinear mixed quasi-variational inequalities N. J. Huang;M. R. Bai;Y. J. Cho;S. M. Kang
  4. Math. Inequal. Appl. A new class of generalized nonlinear mixed quasi-variational inequalities in Banach spaces N. J. Huang;Y. P. Fang;Y. J. Cho
  5. KKM Theory and Applications G. X. Z. Yuan
  6. Computers Math. Appl. v.37 no.10 On the generalized set-valued strongly nonlinear implicit variational inequalities N. J. Huang;Y. P. Liu;Y. Y. Tang;M. R. Bai
  7. SIAM J. Control. Optim. v.34 no.5 Modified projection-type methods for monotone variational inequalities M. V. Solodov;P. Tseng
  8. Comment. Math. Univ. Carolinae v.39 no.1 On monotone nonlinear variational inequality problems R. U. Verma
  9. J. Math. Anal. Appl. v.216 On the generalized implicit quasi-variational inequalities N. J. Huang
  10. Math. Programming v.48 Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications P. T. Harker;J. S. Pang
  11. Variational Inequalities and Network Equilibrium Problems F. Giannessi;A. Maugeri
  12. J. Math. Anal. Appl. v.256 Auxiliary principle and iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities N. J. Huang;C. X. Deng
  13. J. Inequal. Appl. v.5 no.5 Random generalized set-valued strongly nonlinear implicit quasi-variational inequalities Y. J. Cho;N. J. Huang;S. M. Kang
  14. J. Math. Anal. Appl. v.246 Generalized set-valued variational inclusions in Banach spaces S. S. Chang;Y. J. Cho;B. S. Lee;I. H. Jung
  15. Nonlinear Functional Analysis and Its Applications Ⅳ E. Zeidler
  16. Appl. Math. Lett. v.10 no.4 Nonlinear variational inequalities on convex subsets of Banach spaces R. U. Verma
  17. Math. Annal. v.266 Some properties of convex sets related to fixed point theorem K. Fan
  18. Computers Math. Appl. v.35 no.10 A new completely general class of variational inclusions with noncompact valued mappings N. J. Huang
  19. Publ. Math. Debrecen v.53 no.1-2 Generalized pseudo-contractions and nonlinear variational inequalities R. U. Verma
  20. Inequality Problems in Mechanics and Applications P. D. Panagiotopoulos

Cited by

  1. On the Index of Solvability for Variational Inequalities in Banach Spaces vol.16, pp.1, 2008,
  2. The penalty method for generalized multivalued nonlinear variational inequalities in Banach spaces vol.20, pp.8, 2007,