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International Journal of Analysis
Volume 2013 (2013), Article ID 762380, 7 pages
http://dx.doi.org/10.1155/2013/762380
Research Article

Vector Variational-Like Inequalities with Generalized Semimonotone Mappings

Department of Mathematics, BITS Pilani, Dubai Campus, 345055 Dubai, UAE

Received 14 August 2012; Accepted 20 October 2012

Academic Editor: Ying Hu

Copyright © 2013 Suhel Ahmad Khan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. Giannessi, “Theorems of alternative, quadratic programs and complementarity problems,” in Variational Inequalities and Complementarity Problems, R. W. Cottle, F. Giannessi, and J. L. Lions, Eds., pp. 151–186, John Wiley & Sons, New York, NY, USA, 1980. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. G. Y. Chen, “Existence of solutions for a vector variational inequality: an extension of the Hartmann-Stampacchia theorem,” Journal of Optimization Theory and Applications, vol. 74, no. 3, pp. 445–456, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. G. Y. Chen and X. Q. Yang, “The vector complementary problem and its equivalences with the weak minimal element in ordered spaces,” Journal of Mathematical Analysis and Applications, vol. 153, no. 1, pp. 136–158, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. F. Giannessi, Vector Variational Inequalities and Vector Equilibrium, Kluwer Academic Press, 1999.
  5. K. L. Lin, D. P. Yang, and J. C. Yao, “Generalized vector variational inequalities,” Journal of Optimization Theory and Applications, vol. 92, no. 1, pp. 117–126, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. X. Q. Yang, “Vector variational inequality and its duality,” Nonlinear Analysis, vol. 21, no. 11, pp. 869–877, 1993. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. F. Zheng, “Vector variational inequalities with semi-monotone operators,” Journal of Global Optimization, vol. 32, no. 4, pp. 633–642, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. F. E. Browder, “Semi-contract and semi-accretive nonlinear mappings in Banach space,” Bulletin of the American Mathematical Society, vol. 74, pp. 660–665, 1968. View at Google Scholar
  9. Y. Q. Chen, “On the semi-monotone operator theory and applications,” Journal of Mathematical Analysis and Applications, vol. 231, no. 1, pp. 177–192, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. Y. P. Fang and N. J. Huang, “Variational-like inequalities with generalized monotone mappings in Banach spaces,” Journal of Optimization Theory and Applications, vol. 118, no. 2, pp. 327–338, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. F. Usman and S. A. Khan, “A generalized mixed vector variational-like inequality problem,” Nonlinear Analysis, vol. 71, no. 11, pp. 5354–5362, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. D. Goeleven and D. Motreanu, “Eigenvalue and dynamic problems for variational and hemivariational inequalities,” Communications on Applied Nonlinear Analysis, vol. 3, no. 4, pp. 1–21, 1996. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. R. U. Verma, “On monotone nonlinear variational inequality problems,” Commentationes Mathematicae Universitatis Carolinae, vol. 39, no. 1, pp. 91–98, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. R. U. Verma, “Nonlinear variational inequalities on convex subsets of banach spaces,” Applied Mathematics Letters, vol. 10, no. 4, pp. 25–27, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  15. K. Fan, “A generalization of Tychonoff's fixed point theorem,” Mathematische Annalen, vol. 142, no. 3, pp. 305–310, 1961. View at Publisher · View at Google Scholar · View at Scopus
  16. E. Zeidle, Nonlinear Functional Analysis and Its Applications, vol. 4, Springer, Berlin, Germany, 1993.