Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 892641, 7 pages
http://dx.doi.org/10.1155/2014/892641
Research Article

Implicit Multifunction Theorems in Banach Spaces

1School of Management, Fudan University, Shanghai 200433, China
2Department of Mathematics, Luoyang Normal University, Luoyang, Henan 471022, China

Received 31 December 2013; Accepted 21 January 2014; Published 9 March 2014

Academic Editor: Nan-Jing Huang

Copyright © 2014 Ming-ge Yang and Yi-fan Xu. 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. S. M. Robinson, “Stability theory for systems of inequalities, I. Linear systems,” SIAM Journal on Numerical Analysis, vol. 12, no. 5, pp. 754–769, 1975. View at Google Scholar · View at Scopus
  2. S. M. Robinson, “Stability theory for systems of inequalities, II. Differentiable nonlinear systems,” SIAM Journal on Numerical Analysis, vol. 13, no. 4, pp. 497–513, 1976. View at Google Scholar · View at Scopus
  3. S. M. Robinson, “Generalized equations and their solutions, I. Basic theory,” Mathematical Programming Studies, vol. 10, pp. 128–141, 1979. View at Publisher · View at Google Scholar
  4. S. M. Robinson, “Generalized equations and their solutions, II. Applications to nonlinear programming,” Mathematical Programming Studies, vol. 19, pp. 200–221, 1982. View at Google Scholar · View at Scopus
  5. Y. S. Ledyaev and Q. J. Zhu, “Implicit multifunction theorems,” Set-Valued Analysis, vol. 7, no. 3, pp. 209–238, 1999. View at Google Scholar · View at Scopus
  6. H. V. Ngai and M. Théra, “Error bounds and implicit multifunction theorem in smooth Banach spaces and applications to optimization,” Set-Valued Analysis, vol. 12, no. 1-2, pp. 195–223, 2004. View at Google Scholar · View at Scopus
  7. G. M. Lee, N. N. Tam, and N. D. Yen, “Normal coderivative for multifunctions and implicit function theorems,” Journal of Mathematical Analysis and Applications, vol. 338, no. 1, pp. 11–22, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. N. D. Yen and J.-C. Yao, “Point-based sufficient conditions for metric regularity of implicit multifunctions,” Nonlinear Analysis: Theory, Methods and Applications, vol. 70, no. 7, pp. 2806–2815, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. N. Q. Huy and J.-C. Yao, “Stability of implicit multifunctions in Asplund spaces,” Taiwanese Journal of Mathematics, vol. 13, no. 1, pp. 47–65, 2009. View at Google Scholar · View at Scopus
  10. N. Q. Huy and J.-C. Yao, “Metric regularity of parametric generalized inequality systems,” Taiwanese Journal of Mathematics, vol. 14, no. 5, pp. 2107–2123, 2010. View at Google Scholar · View at Scopus
  11. N. H. Chieu, J.-C. Yao, and N. D. Yen, “Relationships between Robinson metric regularity and Lipschitz-like behavior of implicit multifunctions,” Nonlinear Analysis: Theory, Methods and Applications, vol. 72, no. 9-10, pp. 3594–3601, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. T. D. Chuong, “Lipschitz-like property of an implicit multifunction and its applications,” Nonlinear Analysis: Theory, Methods and Applications, vol. 74, no. 17, pp. 6256–6264, 2011. View at Publisher · View at Google Scholar · View at Scopus
  13. T. T. A. Nghia, “A note on implicit multifunction theorems,” Optimization Letters, vol. 8, no. 1, pp. 329–341, 2014. View at Google Scholar
  14. M. G. Yang and N. J. Huang, “Random implicit function theorems in Asplund spaces with applications,” Journal of Nonlinear and Convex Analysis, vol. 14, no. 3, pp. 497–517, 2013. View at Google Scholar
  15. N. Q. Huy, D. S. Kim, and K. V. Ninh, “Stability of Implicit Multifunctions in Banach Spaces,” Journal of Optimization Theory and Applications, vol. 155, pp. 558–571, 2012. View at Publisher · View at Google Scholar · View at Scopus
  16. B. S. Mordukhovich, Variational Analysis and Generalized Differentiation vol I: Basic Theory, Springer, Berlin, Germany, 2006.
  17. B. S. Mordukhovich, Variational Analysis and Generalized Differentiation vol II: Applications, Springer, Berlin, Germany, 2006.
  18. F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, NY, USA, 1983.