Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 176283, 14 pages
http://dx.doi.org/10.1155/2012/176283
Research Article

Existence and Iterative Algorithm of Solutions for a System of Generalized Nonlinear Mixed Variational-Like Inequalities

Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China

Received 29 December 2011; Accepted 16 January 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Yan-Mei Du. 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. G. Stampacchia, “Formes bilinéaires coercitives sur les ensembles convexes,” Les Comptes Rendus de l'Académie des Sciences, vol. 258, pp. 4413–4416, 1964. View at Google Scholar · View at Zentralblatt MATH
  2. Y. Yao, M. A. Noor, and Y.-C. Liou, “Strong convergence of a modified extra-gradient method to the minimum-norm solution of variational inequalities,” Abstract and Applied Analysis, vol. 2012, Article ID 817436, 9 pages, 2012. View at Publisher · View at Google Scholar
  3. L. C. Zeng, S. Schaible, and J.-C. Yao, “Iterative algorithm for generalized set-valued strongly nonlinear mixed variational-like inequalities,” Journal of Optimation Theory and Applications, vol. 124, no. 3, pp. 725–738, 2005. View at Google Scholar
  4. Y. Yao, M. A. Noor, and Y.-C. Liou, “Iterative algorithms for general multi-valued variational inequalities,” Abstract and Applied Analysis, vol. 2012, Article ID 768272, 10 pages, 2012. View at Publisher · View at Google Scholar
  5. Y. Yao, M. A. Noor, and Y.-C. Liou, “Hierarchical convergence of an implicit double-net algorithm for nonexpansive semigroups and variational inequalities,” Fixed Point Theory and Applications, vol. 2011, p. 101, 2011. View at Publisher · View at Google Scholar
  6. M. A. Noor, “Mixed variational-like inequalities,” Communications on Applied Nonlinear Analysis, vol. 1, no. 4, pp. 63–75, 1994. View at Google Scholar · View at Zentralblatt MATH
  7. M. A. Noor, “Iterative schemes for multivalued quasi variational inclusions,” Journal of Global Optimization, vol. 19, no. 2, pp. 141–150, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. X. H. Chen and Y. F. Liu, “A generalized nonlinear variational-like inequality in reflexive Banach spaces,” Journal of Nanjing University Mathematic Biquart, vol. 18, no. 1, pp. 96–103, 2001. View at Google Scholar
  9. J. Parida, M. Sahoo, and A. Kumar, “A variational-like inequality problem,” Bulletin of the Australian Mathematical Society, vol. 39, no. 2, pp. 225–231, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. R. Glowinski, J.-L. Lions, and R. Tremolieres, Numerical Analysis of Variational Inequalities, North-Holland Publishing, New York, NY, USA, 1981.
  11. J. Shen and L.-P. Pang, “A bundle-type auxiliary problem method for solving generalized variational-like inequalities,” Computers & Mathematics with Applications, vol. 55, no. 12, pp. 2993–2998, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. J. Y. Park and J. U. Jeong, “Generalized nonlinear variational-like inequalities in reflexive Banach spaces,” Mathematical Methods in the Applied Sciences, vol. 33, no. 13, pp. 1637–1646, 2010. View at Google Scholar · View at Zentralblatt MATH
  13. M. A. Noor, “Auxiliary principle for generalized mixed variational-like inequalities,” Journal of Mathematical Analysis and Applications, vol. 215, no. 1, pp. 75–85, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. L.-C. Ceng, S.-M. Guu, and J.-C. Yao, “Iterative algorithm for finding approximate solutions of mixed quasi-variational-like inclusions,” Computers & Mathematics with Applications, vol. 56, no. 4, pp. 942–952, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. X. P. Ding, J.-C. Yao, and L.-C. Zeng, “Existence and algorithm of solutions for generalized strongly nonlinear mixed variational-like inequalities in Banach spaces,” Computers & Mathematics with Applications, vol. 55, no. 4, pp. 669–679, 2008. View at Publisher · View at Google Scholar
  16. K. R. Kazmi and F. A. Khan, “Auxiliary problems and algorithm for a system of generalized variational-like inequality problems,” Applied Mathematics and Computation, vol. 187, no. 2, pp. 789–796, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. X. P. Ding, “General algorithm for nonlinear variational-like inequalities in reflexive Banach spaces,” Indian Journal of Pure and Applied Mathematics, vol. 29, no. 2, pp. 109–120, 1998. View at Google Scholar · View at Zentralblatt MATH
  18. C. E. Chidume, K. R. Kazmi, and H. Zegeye, “General auxiliary problem and algorithm for a generalized multi-valued variational-like inequality problem in reflexive Banach spaces,” Applicable Analysis. An International Journal, vol. 82, no. 12, pp. 1099–1109, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. Y. Yao, Y. -C. Liou, and S. M. Kang, “Two-step projection methods for a system of variational inequality problems in Banach spaces,” Journal of Global Optimization. In press. View at Publisher · View at Google Scholar
  20. S. S. Chang and S. W. Xiang, “Existence of solutions for a class of quasibilinear variational inequalities,” Journal of Systems Science and Mathematical Sciences, vol. 16, no. 2, pp. 136–140, 1996. View at Google Scholar