- 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 310796, 6 pages
On Abstract Economies and Their Applications
Department of Mathematics, National Taiwan Normal University, No. 88, Section 4, Ting-Chou Road, Taipei 116, Taiwan
Received 10 July 2013; Accepted 22 August 2013
Academic Editor: Wei-Shih Du
Copyright © 2013 Chien-Hao Huang and Liang-Ju Chu. 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.
- W. Shafer and H. Sonnenschein, “Equilibrium in abstract economies without ordered preferences,” Journal of Mathematical Economics, vol. 2, no. 3, pp. 345–348, 1975.
- X. P. Ding, “Fixed points, minimax inequalities and equilibria of noncompact abstract economies,” Taiwanese Journal of Mathematics, vol. 2, no. 1, pp. 25–55, 1998.
- X. P. Ding, W. K. Kim, and K.-K. Tan, “Equilibria of noncompact generalized games with -majorized preference correspondences,” Journal of Mathematical Analysis and Applications, vol. 164, no. 2, pp. 508–517, 1992.
- L. G. Epstein and S. Ji, “Ambiguous volatility and asset pricing in continuous time,” CIRANO Working Papers 2012s-29, CIRANO, 2012.
- N. J. Huang, “The existence of equilibria for generalized abstract economics,” Indian Journal of Pure and Applied Mathematics, vol. 29, no. 8, pp. 801–809, 1998.
- N. J. Huang, “Some new equilibrium theorems for abstract economies,” Applied Mathematics Letters, vol. 11, no. 1, pp. 41–45, 1998.
- W. K. Kim and K.-K. Tan, “New existence theorems of equilibria and applications,” Nonlinear Analysis: Theory, Methods and Applications, vol. 47, no. 1, pp. 531–542, 2001.
- L.-J. Lin, L.-F. Chen, and Q. H. Ansari, “Generalized abstract economy and systems of generalized vector quasi-equilibrium problems,” Journal of Computational and Applied Mathematics, vol. 208, no. 2, pp. 341–353, 2007.
- Z.-F. Shen, “Maximal element theorems of -majorized correspondence and existence of equilibrium for abstract economies,” Journal of Mathematical Analysis and Applications, vol. 256, no. 1, pp. 67–79, 2001.
- S. Al-Homidan and Q. H. Ansari, “Fixed point theorems on product topological semilattice spaces, generalized abstract economies and systems of generalized vector quasi-equilibrium problems,” Taiwanese Journal of Mathematics, vol. 15, no. 1, pp. 307–330, 2011.
- K.-K. Tan and X.-Z. Yuan, “Lower semicontinuity of multivalued mappings and equilibrium points,” in World Congress of Nonlinear Analysts '92: Proceedings of the 1st World Congress of Nonlinear Analysts, vol. 8, pp. 1849–1860, Walter De Gruyter, Berlin, Germany, 1996.
- E. Tarafdar and P. J. Watson, “Coincidence and the Fan-Glicksberg fixed point theorem in locally H-convex uniform spaces,” Tech. Rep., The University of Queensland, 1997.
- X. Wu and Z.-F. Shen, “Equilibrium of abstract economy and generalized quasi-variational inequality in -spaces,” Topology and its Applications, vol. 153, no. 1, pp. 123–132, 2005.
- G. X.-Z. Yuan and E. Tarafdar, “Maximal elements and equilibria of generalized games for -majorized and condensing correspondences,” International Journal of Mathematics and Mathematical Sciences, vol. 22, no. 1, pp. 179–189, 1999.
- J. L. Kelley, General Topology, Springer, New York, NY, USA, 1975.
- Y.-L. Wu, C.-H. Huang, and L.-J. Chu, “An extension of Mehta theorem with applications,” Journal of Mathematical Analysis and Applications, vol. 391, no. 2, pp. 489–495, 2012.
- C. D. Horvath, “Contractibility and generalized convexity,” Journal of Mathematical Analysis and Applications, vol. 156, no. 2, pp. 341–357, 1991.
- N. C. Yannelis and N. D. Prabhakar, “Existence of maximal elements and equilibria in linear topological spaces,” Journal of Mathematical Economics, vol. 12, no. 3, pp. 233–245, 1983.
- X. Wu and G. X.-Z. Yuan, “On equilibrium problem of abstract economy, generalized quasi-variational inequality, and an optimization problem in locally -convex spaces,” Journal of Mathematical Analysis and Applications, vol. 282, no. 2, pp. 495–504, 2003.
- J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis, John Wiley & Sons, New York, NY, USA, 1984.
- H. Kneser, “Sur un théorème fondamental de la théorie des jeux,” Comptes Rendus de l'Académie des Sciences, vol. 234, pp. 2418–2420, 1952.