• Published : 2007.07.31


Some existence theorems of solutions of a new class of generalized vector F-implicit complementarity problems with the corresponding generalized vector F-implicit variational inequality problems were established.


vector F-implicit complementarity problem;vector F-implicit variational inequality;KKM mapping;process


  1. J.-P. Aubin and H. Frankowska, Set- Valued Analysis, Birkhiiuser Boston (1990)
  2. A. Bensoussan, Variational inequalities and optimal stopping time problems. D. L. Russel ed. : Calculus of Variations and Control Theory, Academic Press (1976), 219-244
  3. A. Carbone, A note on complementarity problem, Internat. J. Math. Math. Sci. 21 (1998), no. 3, 621-623
  4. S. S. Chang and N. J. Huang, Generalized multivalued implicit complementarity problems in Hilbert spaces, Math. Japonica 36(1991), no. 6, 1093-1100
  5. G. Y. Chen and X. Q. Yang, The vector complementarity problems and its equivalences with the weak minimal element in ordered spaces, J. Math. Anal. Appl, 153 (1990), 136-158
  6. R. W. Cottle and G. B. Danzig, Complementarity pivot theory of mathematical programming, Linear Algebra Appl. 1 (1968), 103-125
  7. R. W. Cottle and J. C. Yao, Pseudo-monotone complementarity problems in Hilbert space, J. Opti, Th. & Appl. 75 (1992), no. 2, 281-295
  8. K. Fan, A generalization of Tychonoff's fixed point theorem, Math. Ann. 142 (1961), 305-310
  9. Y. P. Fang and N. J. Huang, The vector F-complementarity problem with demipseudomonotone mappings in Banach spaces, Appl. Math. Lett. 16 (2003), 1019-1024
  10. W. Guo, Implicit complementarity problems in Banach spaces, Northeast. Math. J. 13 (1997) 335-339
  11. G. Isac, A special variational inequality and the implicit complementarity problems, J. Fac. Sci. Univ. Tokyo 37 (1990), 109-127
  12. G. Isac, Complementarity Problems, Springer-Verlag, New York, 1992
  13. G. Isac, A generalization of K aramardian's condition in complementarity theory, Non-linear Analysis Forum 4 (1999), 49-63
  14. G. Isac, On the implicit complementarity problem in Hilbert spaces, Bull. Australian Math. Soc. 32 (1985), 251-260
  15. G. Isac, Topological Methods in Complementarity Theory, Kluwer Academic Publishers, Dordrecht, Boston, London, 2000
  16. G. Isac and J. Li, Complementarity problems, Karamardian's condition and a generalization of Harker-Pang condition, Nonlinear Analysis Forum 6 (2001), no. 2, 383-390
  17. S. Karamardian, Generalized complementarity problem, J. Optim. Theory Appl. 8 (1971), 161-168
  18. B. S. Lee, M. Firdosh Khan, and Salahuddin, Vector F-implicit complementarity problems with corresponding variational inequality problems, Appl. Math. Lett. 20 (2007), 433-438
  19. C. E. Lemke, Bimatrix equilibrium points and mathematical programming, Management Sci. 11 (1965), 681-689
  20. J. Li and N. J. Huang, Vector F -implicit complementarity problems in Banach spaces, Appl. Math. Lett. 19 (2006), 467-471
  21. S. Zhang and Y. Shu, Complementarity problems with applications to mathematical programming, Acta Math. Appl, Sinica 15 (1992) 380-388
  22. I. Capuzzo-Dolcetta and U. Mosco, Implicit complementarity problems and quasivariational inequalities, R. W. Cottle, R. Giannessi and J. L. Lions ed. : Variational Inequalities and Complementarity Problems, Theory and Applications, John Wiley and Sons (1990), 75-87
  23. N. J. Huang and J. Li, F-implicit complementarity problems in Banach spaces, Z. Anal. Anwendungen 23 (2004), 293-302
  24. G. Isac, Condition $\(S)_{1}^{+}$Altman's condition and the scalar asymptotic derivative: ap- plications to complementarity theory, Nonlinear Analysis Forum 5 (2000), 1-13
  25. H. Y. Yin, C. X. Xu, and Z. X. Zhang, The complementarity problems and its equivalence with the least element problem, Acta Math. Sinica 44 (2001), 679-686