Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SOME VECTOR IMPLICIT COMPLEMENTARITY PROBLEMS WITH CORRESPONDING VARIATIONAL INEQUALITY PROBLEMS

  • Published : 2007.07.31
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Abstract

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.

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References

  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. 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
  4. A. Carbone, A note on complementarity problem, Internat. J. Math. Math. Sci. 21 (1998), no. 3, 621-623 https://doi.org/10.1155/S0161171298000878
  5. S. S. Chang and N. J. Huang, Generalized multivalued implicit complementarity problems in Hilbert spaces, Math. Japonica 36(1991), no. 6, 1093-1100
  6. 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 https://doi.org/10.1016/0022-247X(90)90270-P
  7. R. W. Cottle and G. B. Danzig, Complementarity pivot theory of mathematical programming, Linear Algebra Appl. 1 (1968), 103-125 https://doi.org/10.1016/0024-3795(68)90052-9
  8. R. W. Cottle and J. C. Yao, Pseudo-monotone complementarity problems in Hilbert space, J. Opti, Th. & Appl. 75 (1992), no. 2, 281-295 https://doi.org/10.1007/BF00941468
  9. K. Fan, A generalization of Tychonoff's fixed point theorem, Math. Ann. 142 (1961), 305-310 https://doi.org/10.1007/BF01353421
  10. 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 https://doi.org/10.1016/S0893-9659(03)90089-9
  11. W. Guo, Implicit complementarity problems in Banach spaces, Northeast. Math. J. 13 (1997) 335-339
  12. N. J. Huang and J. Li, F-implicit complementarity problems in Banach spaces, Z. Anal. Anwendungen 23 (2004), 293-302
  13. G. Isac, A special variational inequality and the implicit complementarity problems, J. Fac. Sci. Univ. Tokyo 37 (1990), 109-127
  14. G. Isac, Complementarity Problems, Springer-Verlag, New York, 1992
  15. G. Isac, A generalization of K aramardian's condition in complementarity theory, Non-linear Analysis Forum 4 (1999), 49-63
  16. G. Isac, On the implicit complementarity problem in Hilbert spaces, Bull. Australian Math. Soc. 32 (1985), 251-260 https://doi.org/10.1017/S000497270000993X
  17. 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
  18. G. Isac, Topological Methods in Complementarity Theory, Kluwer Academic Publishers, Dordrecht, Boston, London, 2000
  19. 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
  20. S. Karamardian, Generalized complementarity problem, J. Optim. Theory Appl. 8 (1971), 161-168 https://doi.org/10.1007/BF00932464
  21. 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 https://doi.org/10.1016/j.aml.2006.05.010
  22. C. E. Lemke, Bimatrix equilibrium points and mathematical programming, Management Sci. 11 (1965), 681-689 https://doi.org/10.1287/mnsc.11.7.681
  23. J. Li and N. J. Huang, Vector F -implicit complementarity problems in Banach spaces, Appl. Math. Lett. 19 (2006), 467-471 https://doi.org/10.1016/j.aml.2005.07.003
  24. 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
  25. S. Zhang and Y. Shu, Complementarity problems with applications to mathematical programming, Acta Math. Appl, Sinica 15 (1992) 380-388