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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 419053, 7 pages
http://dx.doi.org/10.1155/2013/419053
Research Article

Well-Posedness for Generalized Set Equilibrium Problems

Department of Occupational Safety and Health, College of Public Health, China Medical University, Taichung 40421, Taiwan

Received 14 July 2013; Accepted 13 September 2013

Academic Editor: Jen-Chih Yao

Copyright © 2013 Yen-Cherng Lin. 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. A. N. Tihonov, “Stability of a problem of optimization of functionals,” Akademija Nauk SSSR, vol. 6, pp. 631–634, 1966. View at MathSciNet
  2. L. C. Ceng and Y. C. Lin, “Metric characterizations of α-well-posedness for a system of mixed quasivariational-like inequalities in Banach spaces,” Journal of Applied Mathematics, vol. 2012, Article ID 264721, 22 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  3. A. L. Dontchev and T. Zolezzi, Well-Posed Optimization Problems, Springer, Berlin, Germany, 1993. View at MathSciNet
  4. E. Bednarczuk and J.-P. Penot, “Metrically well-set minimization problems,” Applied Mathematics and Optimization, vol. 26, no. 3, pp. 273–285, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. G. P. Crespi, A. Guerraggio, and M. Rocca, “Well posedness in vector optimization problems and vector variational inequalities,” Journal of Optimization Theory and Applications, vol. 132, no. 1, pp. 213–226, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. Furi and A. Vignoli, “About well-posed minimization problems for functionals in metric spaces,” Journal of Optimization Theory and Applications, vol. 5, no. 3, pp. 225–229, 1970. View at Publisher · View at Google Scholar
  7. T. Zolezzi, “Well-posedness criteria in optimization with application to the calculus of variations,” Nonlinear Analysis:Theory, Methods & Applications, vol. 25, no. 5, pp. 437–453, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. E. Miglierina and E. Molho, “Well-posedness and convexity in vector optimization,” Mathematical Methods of Operations Research, vol. 58, no. 3, pp. 375–385, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. E. Bednarczuk, “An approach to well-posedness in vector optimization: consequences to stability,” Control and Cybernetics, vol. 23, no. 1-2, pp. 107–122, 1994. View at Zentralblatt MATH · View at MathSciNet
  10. M. Bianchi, G. Kassay, and R. Pini, “Well-posedness for vector equilibrium problems,” Mathematical Methods of Operations Research, vol. 70, no. 1, pp. 171–182, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. L. C. Ceng, N. Hadjisavvas, S. Schaible, and J. C. Yao, “Well-posedness for mixed quasivariational-like inequalities,” Journal of Optimization Theory and Applications, vol. 139, no. 1, pp. 109–125, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. L. C. Ceng and J. C. Yao, “Well-posedness of generalized mixed variational inequalities, inclusion problems and fixed-point problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 12, pp. 4585–4603, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y.-P. Fang, N.-J. Huang, and J.-C. Yao, “Well-posedness of mixed variational inequalities, inclusion problems and fixed point problems,” Journal of Global Optimization, vol. 41, no. 1, pp. 117–133, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. K. Kimura, Y.-C. Liou, S.-Y. Wu, and J.-C. Yao, “Well-posedness for parametric vector equilibrium problems with applications,” Journal of Industrial and Management Optimization, vol. 4, no. 2, pp. 313–327, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. L. Q. Anh, P. Q. Khanh, D. T. M. van, and J.-C. Yao, “Well-posedness for vector quasiequilibria,” Taiwanese Journal of Mathematics, vol. 13, no. 2B, pp. 713–737, 2009. View at Zentralblatt MATH · View at MathSciNet
  16. C. Berge, Topological Spaces, Macmillan, New York, NY, USA, 1963.
  17. J.-P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin, Germany, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  18. F. Ferro, “Optimization and stability results through cone lower semicontinuity,” Set-Valued Analysis, vol. 5, no. 4, pp. 365–375, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. Y.-C. Lin, Q. H. Ansari, and H.-C. Lai, “Minimax theorems for set-valued mappings under cone-convexities,” Abstract and Applied Analysis, vol. 2012, Article ID 310818, 26 pages, 2012. View at Zentralblatt MATH · View at MathSciNet