Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2012, Article ID 236413, 14 pages
http://dx.doi.org/10.1155/2012/236413
Research Article

Hölder Continuity of Solutions to Parametric Generalized Vector Quasiequilibrium Problems

1School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
2College of Science, Chongqing Jiao Tong University, Chongqing 400074, China

Received 2 October 2011; Accepted 2 December 2011

Academic Editor: Svatoslav Staněk

Copyright © 2012 Z. Y. Peng. 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, Ed., Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, vol. 38 of Nonconvex Optimization and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.
  2. F. Giannessi, A. Maugeri, and P. M. Pardalos, Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Methods, Kluwer Acad. Publ., Dordrecht, The Netherlands, 2001.
  3. G.-Y. Chen, X. Huang, and X. Yang, Vector Optimization: Set-Valued and Variational Analysis, vol. 541 of Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, Germany, 2005.
  4. Y. H. Cheng and D. L. Zhu, “Global stability results for the weak vector variational inequality,” Journal of Global Optimization, vol. 32, no. 4, pp. 543–550, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. L. Q. Anh and P. Q. Khanh, “Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems,” Journal of Mathematical Analysis and Applications, vol. 294, no. 2, pp. 699–711, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. L. Q. Anh and P. Q. Khanh, “On the stability of the solution sets of general multivalued vector quasiequilibrium problems,” Journal of Optimization Theory and Applications, vol. 135, no. 2, pp. 271–284, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. N. J. Huang, J. Li, and H. B. Thompson, “Stability for parametric implicit vector equilibrium problems,” Mathematical and Computer Modelling, vol. 43, no. 11-12, pp. 1267–1274, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. C. R. Chen, S. J. Li, and K. L. Teo, “Solution semicontinuity of parametric generalized vector equilibrium problems,” Journal of Global Optimization, vol. 45, no. 2, pp. 309–318, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. C. R. Chen and S. J. Li, “On the solution continuity of parametric generalized systems,” Pacific Journal of Optimization, vol. 6, no. 1, pp. 141–151, 2010. View at Google Scholar · View at Zentralblatt MATH
  10. X. H. Gong and J. C. Yao, “Lower semicontinuity of the set of efficient solutions for generalized systems,” Journal of Optimization Theory and Applications, vol. 138, no. 2, pp. 197–205, 2008. View at Publisher · View at Google Scholar
  11. X. H. Gong, “Continuity of the solution set to parametric weak vector equilibrium problems,” Journal of Optimization Theory and Applications, vol. 139, no. 1, pp. 35–46, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. K. Kimura and J.-C. Yao, “Sensitivity analysis of solution mappings of parametric vector quasi-equilibrium problems,” Journal of Global Optimization, vol. 41, no. 2, pp. 187–202, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. L. Q. Anh and P. Q. Khanh, “Sensitivity analysis for weak and strong vector quasiequilibrium problems,” Vietnam Journal of Mathematics, vol. 37, no. 2-3, pp. 237–253, 2009. View at Google Scholar · View at Zentralblatt MATH
  14. N. D. Yên, “Hölder continuity of solutions to a parametric variational inequality,” Applied Mathematics and Optimization, vol. 31, no. 3, pp. 245–255, 1995. View at Publisher · View at Google Scholar
  15. M. Ait Mansour and H. Riahi, “Sensitivity analysis for abstract equilibrium problems,” Journal of Mathematical Analysis and Applications, vol. 306, no. 2, pp. 684–691, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. M. Bianchi and R. Pini, “A note on stability for parametric equilibrium problems,” Operations Research Letters, vol. 31, no. 6, pp. 445–450, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. M. Bianchi and R. Pini, “Sensitivity for parametric vector equilibria,” Optimization, vol. 55, no. 3, pp. 221–230, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. L. Q. Anh and P. Q. Khanh, “On the Hölder continuity of solutions to parametric multivalued vector equilibrium problems,” Journal of Mathematical Analysis and Applications, vol. 321, no. 1, pp. 308–315, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. L. Q. Anh and P. Q. Khanh, “Uniqueness and Hölder continuity of the solution to multivalued equilibrium problems in metric spaces,” Journal of Global Optimization, vol. 37, no. 3, pp. 449–465, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. L. Q. Anh and P. Q. Khanh, “Sensitivity analysis for multivalued quasiequilibrium problems in metric spaces: Hölder continuity of solutions,” Journal of Global Optimization, vol. 42, no. 4, pp. 515–531, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. G. M. Lee, D. S. Kim, B. S. Lee, and N. D. Yen, “Vector variational inequality as a tool for studying vector optimization problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 34, no. 5, pp. 745–765, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. M. Ait Mansour and D. Aussel, “Quasimonotone variational inequalities and quasiconvex programming: quantitative stability,” Pacific Journal of Optimization, vol. 2, no. 3, pp. 611–626, 2006. View at Google Scholar · View at Zentralblatt MATH
  23. S. J. Li, X. B. Li, and K. L. Teo, “The Hölder continuity of solutions to generalized vector equilibrium problems,” European Journal of Operational Research, vol. 199, no. 2, pp. 334–338, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. S. J. Li, C. R. Chen, X. B. Li, and K. L. Teo, “Hölder continuity and upper estimates of solutions to vector quasiequilibrium problems,” European Journal of Operational Research, vol. 210, no. 2, pp. 148–157, 2011. View at Publisher · View at Google Scholar
  25. S. J. Li and X. B. Li, “Hölder continuity of solutions to parametric weak generalized Ky Fan inequality,” Journal of Optimization Theory and Applications, vol. 149, no. 3, pp. 540–553, 2011. View at Publisher · View at Google Scholar
  26. L. Q. Anh and P. Q. Khanh, “Hölder continuity of the unique solution to quasiequilibrium problems in metric spaces,” Journal of Optimization Theory and Applications, vol. 141, no. 1, pp. 37–54, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH