East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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VECTOR F-COMPLEMENTARITY PROBLEMS WITH g-DEMI-PSEUDOMONOTONE MAPPINGS IN BANACH SPACES

  • Received : 2009.11.19
  • Accepted : 2010.05.01
  • Published : 2010.05.31
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Abstract

In this paper, a class of g-demi-pseudomonotone mappings is introduced and the solvability of a class of generalized vector F-complementarity problems with the mappings in Banach spaces is considered.

Keywords

References

  1. Y. Q. Chen, On the semi-monotone operator theory and applications, J. Math. Anal. Appl. 231 (1999), 177-192. https://doi.org/10.1006/jmaa.1998.6245
  2. G. Y. Chen and X. Q. Yang, The vector complementarity problem 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
  3. K. Fan, Some properties of convex sets related to xed point theorems, Math. Ann. 266 (1984), 519-537. https://doi.org/10.1007/BF01458545
  4. Y. P. Fang and N. J. Huang, The vector F-complementarity problems with demipseu- domonotone mappings in Banach spaces, Appl. Math. Lett. 16 (2003), 1019-1024. https://doi.org/10.1016/S0893-9659(03)90089-9
  5. Y. P. Fang and N. J. Huang, Variational-like inequalities with generalized monotone mappings in Banach spaces, J. Optim. Th. Appl. 118 (2003), 327-338. https://doi.org/10.1023/A:1025499305742
  6. I. Glicksberg, A further generalization of Kakutani xed point theorem with applications to Nash equilibrium points, Proc. Amer. Math. Soc. 36 (1952), 170-174.
  7. N. Hadjesavvas and S. Schaible, A quasimonotone variational inequalities in Banach spaces, J. Optim. Theo. Appl. 90 (1996), 95-111 https://doi.org/10.1007/BF02192248
  8. M. K. Kang, N. J. Huang and B. S. Lee, Generlized pseudomonotone set-valued variational-like inequalities, Indian J. Math. 45 (2003), 251-264.
  9. S. Karamardian, Complementarity over cones with monotone and pseudomonotone maps, J. Optim. Theo. Appl. 18 (1976), 445-454. https://doi.org/10.1007/BF00932654
  10. G. Kassay and J. Kolumban, Variational inequalities given by semi-pseudomonotone mappings, Nonlinear Analysis Forum 5 (2000), 35-50.
  11. D. T. Luc, Existence results for densely pseudomonotone variational inequalities, J. Math. Anal. Appl. 254 (2001), 291-308. https://doi.org/10.1006/jmaa.2000.7278
  12. R. U. Verma, Nonlinear variational inequalities on convex subsets of Banach spaces, Appl. Math. Lett. 10(4) (1997), 25-27. https://doi.org/10.1016/S0893-9659(97)00054-2
  13. H. Y. Yin, C.X. Hu and Z.X. Zhang, The F-complementarity problems and its equiva- lence with the least element problem, Acta Math. Sinica 44(4) (2001), 679-686.
  14. G. X. Z. Yuan, KKM Theorem and Applications in Nonlinear Analysis, Marcel Dekker, New York, 1999.