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Abstract and Applied Analysis
Volume 2012, Article ID 651975, 35 pages
http://dx.doi.org/10.1155/2012/651975
Research Article

Time-Dependent Variational Inequality for an Oligopolistic Market Equilibrium Problem with Production and Demand Excesses

1Department of Mathematics and Applications “R. Caccioppoli”, University of Naples “Federico II”, Via Cintia 80126 Naples, Italy
2Department of Mathematics and Computer Science, University of Catania, Viale A. Doria, 95125 Catania, Italy

Received 2 February 2012; Accepted 20 March 2012

Academic Editor: Kanishka Perera

Copyright © 2012 Annamaria Barbagallo and Paolo Mauro. 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. Barbagallo and P. Mauro, “Evolutionary variational formulation for oligopolistic market equilibrium problems with production excesses,” Journal of Optimization Theory and Applications, vol. 155, no. 1, 2012. View at Publisher · View at Google Scholar
  2. A. Barbagallo and M.-G. Cojocaru, “Dynamic equilibrium formulation of the oligopolistic market problem,” Mathematical and Computer Modelling, vol. 49, no. 5-6, pp. 966–976, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. A. Cournot, Researches Into The Mathematical Principles Of The Theory Of Wealth, MacMillan, London, UK, 1838.
  4. J. F. Nash Jr., “Equilibrium points in n-person games,” Proceedings of the National Academy of Sciences of the United States of America, vol. 36, pp. 48–49, 1950. View at Publisher · View at Google Scholar
  5. J. Nash, “Non-cooperative games,” Annals of Mathematics. Second Series, vol. 54, pp. 286–295, 1951. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. M. J. Beckmann and J. P. Wallace, “Continuous lags and the stability of market equilibrium,” Economica, New Series 36, pp. 58–68, 1969. View at Google Scholar
  7. A. Barbagallo and A. Maugeri, “Memory term for dynamic oligopolistic market equilibrium problem,” Aplimat, Journal of Applied Mathematics, vol. 3, pp. 13–23, 2010. View at Google Scholar
  8. A. Barbagallo, “Regularity results for time-dependent variational and quasi-variational inequalities and application to the calculation of dynamic traffic network,” Mathematical Models & Methods in Applied Sciences, vol. 17, no. 2, pp. 277–304, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. A. Barbagallo, “Regularity results for evolutionary nonlinear variational and quasi-variational inequalities with applications to dynamic equilibrium problems,” Journal of Global Optimization, vol. 40, no. 1-3, pp. 29–39, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. A. Barbagallo, “Existence and regularity of solutions to nonlinear degenerate evolutionary variational inequalities with applications to dynamic network equilibrium problems,” Applied Mathematics and Computation, vol. 208, no. 1, pp. 1–13, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. A. Barbagallo, “On the regularity of retarded equilibrium in time-dependent traffic equilibrium problems,” Nonlinear Analysis, vol. 71, no. 12, pp. e2406–e2417, 2009. View at Publisher · View at Google Scholar
  12. A. Barbagallo and M.-G. Cojocaru, “Continuity of solutions for parametric variational inequalities in Banach space,” Journal of Mathematical Analysis and Applications, vol. 351, no. 2, pp. 707–720, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. A. Barbagallo and A. Maugeri, “Duality theory for the dynamic oligopolistic market equilibrium problem,” Optimization, vol. 60, no. 1-2, pp. 29–52, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. J. M. Borwein and A. S. Lewis, “Partially finite convex programming. I. Quasi relative interiors and duality theory,” Mathematical Programming, vol. 57, no. 1, Ser. B, pp. 15–48, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. A. Maugeri and F. Raciti, “Remarks on infinite dimensional duality,” Journal of Global Optimization, vol. 46, no. 4, pp. 581–588, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. P. Daniele and S. Giuffrè, “General infinite dimensional duality and applications to evolutionary network equilibrium problems,” Optimization Letters, vol. 1, no. 3, pp. 227–243, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. P. Daniele, S. Giuffrè, G. Idone, and A. Maugeri, “Infinite dimensional duality and applications,” Mathematische Annalen, vol. 339, no. 1, pp. 221–239, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. P. Daniele, S. Giuffré, and A. Maugeri, “Remarks on general infinite dimensional duality with cone and equality constraints,” Communications in Applied Analysis, vol. 13, no. 4, pp. 567–577, 2009. View at Google Scholar · View at Zentralblatt MATH
  19. A. Barbagallo and R. Di Vincenzo, “Lipschitz continuity and duality for dynamic oligopolistic market equilibrium problem with memory term,” Journal of Mathematical Analysis and Applications, vol. 382, no. 1, pp. 231–247, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. A. Barbagallo and P. Mauro, “On solving dynamic oligopolistic market equilibrium problems in presence of excesses,” Submitted.
  21. A. Barbagallo, “Advanced results on variational inequality formulation in oligopolistic market equilibrium problem,” FILOMAT. In press.
  22. O. Mangasarian, “Pseudo-convex functions,” Journal of the Society for Industrial and Applied Mathematics Series A, vol. 3, no. 2, pp. 281–290, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. J. Jahn, Introduction to the Theory of Nonlinear Optimization, Springer, Berlin, Germany, 2nd edition, 1996.
  24. A. Maugeri and F. Raciti, “On existence theorems for monotone and nonmonotone variational inequalities,” Journal of Convex Analysis, vol. 16, no. 3-4, pp. 899–911, 2009. View at Google Scholar · View at Zentralblatt MATH
  25. K. Kuratowski, Topology, Academic Press, New York, NY, USA, 1966.
  26. G. Salinetti and R. J.-B. Wets, “On the convergence of sequences of convex sets in finite dimensions,” SIAM Review, vol. 21, no. 1, pp. 18–33, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. G. Salinetti and R. J.-B. Wets, “Addendum: on the convergence of convex sets in finite dimensions,” SIAM Review, vol. 22, p. 86.
  28. A. Maugeri, “Convex programming, variational inequalities, and applications to the traffic equilibrium problem,” Applied Mathematics and Optimization, vol. 16, no. 2, pp. 169–185, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  29. P. Daniele and A. Maugeri, “The economic model for demand-supply problems,” in Equilibrium Problems and Variational Models, P. Daniele, F. Giannessi, and A. Maugeri, Eds., pp. 61–78, Kluwer Academic, Boston, Mass, USA, 2002. View at Google Scholar
  30. P. Daniele, “Evolutionary variational inequalities and economic models for demand-supply markets,” Mathematical Models & Methods in Applied Sciences, vol. 13, no. 4, pp. 471–489, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH