Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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MIXED VECTOR FQ-IMPLICIT VARIATIONAL INEQUALITY WITH LOCAL NON-POSITIVITY

  • Published : 2009.07.31
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Abstract

This paper introduces a local non-positivity of two set-valued mappings (F,Q) and considers the existences and properties of solutions for set-valued mixed vector FQ-implicit variational inequality problems and set-valued mixed vector FQ-complementarity problems in the neighborhood of a point belonging to an underlined domain K of the set-valued mappings, where the neighborhood is contained in K. This paper generalizes and extends many results in [1, 3-7].

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References

  1. 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
  2. F. Ferro, A minimax theorem for vector-valued functions, J. Optim, Theory Appl. 60 (1989), 19–31 https://doi.org/10.1007/BF00938796
  3. N. J. Huang and J. Li, F-implicit complementarity problems in Banach spaces, Z. Anal. Anwendungen 23 (2004), 293–302
  4. B. S. Lee, Mixed vector FQ-implicit variational inequalities with FQ-complementatity problems, submitted
  5. B. S. Lee, M. F. 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
  6. J. Li and N. J. Huang, Vector F-implicit complementarity problems in Banach spaces, Appl. Math. Lett. 19 (2006), 464–471 https://doi.org/10.1016/j.aml.2005.07.003
  7. H. Y. Yin, C. X. Xu, and Z. X. Zhang, The F-complementarity problems and its equivalence with the least element problem, Acta Math. Sinica 44 (2001), 679–686