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Nash points, Ky Fan inequality and equilibria of abstract economies in Max-Plus and -convexity
- Source :
-
Journal of Mathematical Analysis & Applications . May2008, Vol. 341 Issue 1, p188-199. 12p. - Publication Year :
- 2008
-
Abstract
- Abstract: -convexity was introduced in [W. Briec, C. Horvath, -convexity, Optimization 53 (2004) 103–127]. Separation and Hahn–Banach like theorems can be found in [G. Adilov, A.M. Rubinov, -convex sets and functions, Numer. Funct. Anal. Optim. 27 (2006) 237–257] and [W. Briec, C.D. Horvath, A. Rubinov, Separation in -convexity, Pacific J. Optim. 1 (2005) 13–30]. We show here that all the basic results related to fixed point theorems are available in -convexity. Ky Fan inequality, existence of Nash equilibria and existence of equilibria for abstract economies are established in the framework of -convexity. Monotone analysis, or analysis on Maslov semimodules [V.N. Kolokoltsov, V.P. Maslov, Idempotent Analysis and Its Applications, Math. Appl., vol. 401, Kluwer Academic, 1997; V.P. Litvinov, V.P. Maslov, G.B. Shpitz, Idempotent functional analysis: An algebraic approach, Math. Notes 69 (2001) 696–729; V.P. Maslov, S.N. Samborski (Eds.), Idempotent Analysis, Advances in Soviet Mathematics, Amer. Math. Soc., Providence, RI, 1992], is the natural framework for these results. From this point of view Max-Plus convexity and -convexity are isomorphic Maslov semimodules structures over isomorphic semirings. Therefore all the results of this paper hold in the context of Max-Plus convexity. [Copyright &y& Elsevier]
- Subjects :
- *EQUILIBRIUM
*INTEGRAL theorems
*ISOMORPHISM (Mathematics)
*MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 341
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 30025952
- Full Text :
- https://doi.org/10.1016/j.jmaa.2007.09.056