- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 916089, 8 pages
Existence of Solutions for Generalized Vector Quasi-Equilibrium Problems by Scalarization Method with Applications
1College of Applied Science, Beijing University of Technology, Beijing 100124, China
2College of Mathematics, Jilin Normal University, Siping, Jilin 136000, China
Received 26 November 2012; Accepted 6 February 2013
Academic Editor: Ngai-Ching Wong
Copyright © 2013 De-ning Qu and Cao-zong Cheng. 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.
- X. H. Gong, “Scalarization and optimality conditions for vector equilibrium problems,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 73, no. 11, pp. 3598–3612, 2010.
- G. Y. Chen, X. Q. Yang, and H. Yu, “A nonlinear scalarization function and generalized quasi-vector equilibrium problems,” Journal of Global Optimization, vol. 32, no. 4, pp. 451–466, 2005.
- Q. H. Ansari and F. Flores-Bazán, “Recession methods for generalized vector equilibrium problems,” Journal of Mathematical Analysis and Applications, vol. 321, no. 1, pp. 132–146, 2006.
- S. J. Li and P. Zhao, “A method of duality for a mixed vector equilibrium problem,” Optimization Letters, vol. 4, no. 1, pp. 85–96, 2010.
- 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.
- C. Gerth and P. Weidner, “Nonconvex separation theorems and some applications in vector optimization,” Journal of Optimization Theory and Applications, vol. 67, no. 2, pp. 297–320, 1990.
- G. Y. Chen and X. Q. Yang, “Characterizations of variable domination structures via nonlinear scalarization,” Journal of Optimization Theory and Applications, vol. 112, no. 1, pp. 97–110, 2002.
- N. J. Huang, J. Li, and J. C. Yao, “Gap functions and existence of solutions for a system of vector equilibrium problems,” Journal of Optimization Theory and Applications, vol. 133, no. 2, pp. 201–212, 2007.
- J. Li and N. J. Huang, “An extension of gap functions for a system of vector equilibrium problems with applications to optimization problems,” Journal of Global Optimization, vol. 39, no. 2, pp. 247–260, 2007.
- D. N. Qu and X. P. Ding, “Some quasi-equilibrium problems for multimaps,” Journal of Sichuan Normal University. Natural Science Edition, vol. 30, no. 2, pp. 173–177, 2007.
- D. T. Luc, Theory of Vector Optimization, vol. 319 of Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, Germany, 1989.
- W. Rudin, Functional Analysis, International Series in Pure and Applied Mathematics, McGraw-Hill, New York, NY, USA, 2nd edition, 1991.
- J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis, John Wiley & Sons, New York, NY, USA, 1984.
- L. J. Lin and Z. T. Yu, “On some equilibrium problems for multimaps,” Journal of Computational and Applied Mathematics, vol. 129, no. 1-2, pp. 171–183, 2001.
- J. P. Aubin and A. Cellina, Differential Inclusion, Springer, Berlin, Germany, 1994.
- P. H. Sach and L. A. Tuan, “New scalarizing approach to the stability analysis in parametric generalized Ky Fan inequality problems,” Journal of Optimization Theory and Applications, 2012.
- F. E. Browder, “The fixed point theory of multi-valued mappings in topological vector spaces,” Mathematische Annalen, vol. 177, pp. 283–301, 1968.
- G. M. Lee, D. S. Kim, B. S. Lee, and S. J. Cho, “Generalized vector variational inequality and fuzzy extension,” Applied Mathematics Letters, vol. 6, no. 6, pp. 47–51, 1993.
- S. Park, B. S. Lee, and G. M. Lee, “A general vector-valued variational inequality and its fuzzy extension,” International Journal of Mathematics and Mathematical Sciences, vol. 21, no. 4, pp. 637–642, 1998.
- F. Giannessi, “Theorems of alternative, quadratic programs and complementarity problems,” in Variational Inequality Complementary Problems, R. W. Cottle, F. Giannessi, and J. L. Lions, Eds., pp. 151–186, John Wiley & Sons, New York, NY, USA, 1980.
- X. Q. Yang, “Vector variational inequality and its duality,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 21, no. 11, pp. 869–877, 1993.
- X. Q. Yang and C. J. Goh, “On vector variational inequalities: application to vector equilibria,” Journal of Optimization Theory and Applications, vol. 95, no. 2, pp. 431–443, 1997.