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Stability of Generalized Convexity and Monotonicity

  • P. T. An

Abstract

It was shown that well-known kinds of generalized convex functions (generalized monotone maps, respectively) are often not stable with respect to the property they have to keep during the generalization. Then the so-called s-quasiconvex functions, s-quasimonotone maps and strictly s-quasiconvex functions were introduced in Optimization, vol.38, vol.55 and Journal of Inequalities in Pure and Applied Mathematics, vol.127, respectively. In this paper, some stability properties of such functions and a use of s-quasimonotonicity in an economics model are presented. Furthermore, an algorithm for finding the stability index for strict s-quasiconvexity of a given continuously twice differentiable function on is presented.

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References

  1. 1.
    An, P.T. (2006): Stability of generalized monotone maps with respect to their characterizations. Optimization, 55, pp. 289-299zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    . An, P.T. (2006): A new kind of stable generalized convex functions. Journal of Inequalities in Pure and Applied Mathematics, 127(3), electronicGoogle Scholar
  3. 3.
    An, P.T. and Binh, V.T.T.: Stability of excess demand functions with respect to a strong version of Wald’s axiom. In Workshop “Small open economies in a globalised world”, Rimini, Italy, 29.8-2.9.2006, submitted for publicationGoogle Scholar
  4. 4.
    Brighi, L. (2004): A strong criterion for the Weak Weak Axiom. Journal of Mathematical Economics, 40, pp. 93-103zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Debreu, G. (1959): Theory of Value. Yale University Press, New Haven and LondonzbMATHGoogle Scholar
  6. 6.
    Hildenbrand, W. and Jerison, M. (1989): The demand theory of the weak axioms of revealed preference. Economics Letters, 29, pp. 209-213CrossRefMathSciNetGoogle Scholar
  7. 7.
    Houthakker, H.S. (1953): Revealed preference and the utility function. Economica, 17, pp. 159-174CrossRefMathSciNetGoogle Scholar
  8. 8.
    Karamardian, S. and Schaible, S. (1990): Seven kinds of generalized monotone maps. Journal of Optimization Theory and Applications, 66, pp. 37-46zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Karamardian, S. Schaible, S. and Crouzeix, J.P. (1993): Characterizations geneenralized monotone maps. Journal of Optimization Theory and Applications, 76, pp. 399-413zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Kinderlehrer, D. and Stampacchia, G. (1980): An Introduction to Variational Inequalities and Their Applications. Academic, New YorkzbMATHGoogle Scholar
  11. 11.
    John, R. (1998): Variational inequalities and pseudomonotone functions: some characterizations. In: Crouzeix, J.-P. et al. (ed) Generalized Convexity, Generalized Monotonicity. Kluwer, Dordrecht Boston London, 291-301Google Scholar
  12. 12.
    Mossin, A. (1972): A mean demand function and individual demand functions confronted with the weak and the strong axioms of revealed preference: an empirical test. Economica, 40, pp. 177-192Google Scholar
  13. 13.
    Ponstein, J. (1967): Seven kinds of convexity. SIAM Review, 9, pp. 115-119zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Phu, H.X. and An, P.T. (1996): Stable generalization of convex functions. Optimization, 38, pp. 309-318zbMATHCrossRefMathSciNetGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2008

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  • P. T. An

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