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Constructive Utility Functions on Banach spaces


  • Jose C. R. Alcantud

    (Universidad de Salamanca)

  • Ghanshyam B. Mehta

    (University of Queensland)


In this paper we prove the existence of continuous order-preserving functions on subsets of ordered Banach spaces using a constructive approach.

Suggested Citation

  • Jose C. R. Alcantud & Ghanshyam B. Mehta, 2005. "Constructive Utility Functions on Banach spaces," Microeconomics 0502003, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpmi:0502003
    Note: Type of Document - pdf; pages: 10

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    References listed on IDEAS

    1. Brown, Donald J & Lewis, Lucinda M, 1981. "Myopic Economic Agents," Econometrica, Econometric Society, vol. 49(2), pages 359-368, March.
    2. Ghanshyam Mehta, 1991. "The Euclidean Distance Approach to Continuous Utility Functions," The Quarterly Journal of Economics, Oxford University Press, vol. 106(3), pages 975-977.
    3. Mehta, Ghanshyam, 1988. "Some general theorems on the existence of order-preserving functions," Mathematical Social Sciences, Elsevier, vol. 15(2), pages 135-143, April.
    4. Mas-Colell, Andreu, 1975. "A model of equilibrium with differentiated commodities," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 263-295.
    5. Mehta, Ghanshyam B. & Monteiro, Paulo Klinger, 1996. "Infinite-dimensional utility representation theorems," Economics Letters, Elsevier, vol. 53(2), pages 169-173, November.
    6. Herden, Gerhard & Mehta, Ghanshyam B, 1996. "Open Gaps, Metrization and Utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 541-546, April.
    7. A. F. Beardon, 1997. "Utility representation of continuous preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 369-372.
    8. Alcantud, J. C. R. & Manrique, A., 2001. "Continuous representation by a money-metric function," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 365-373, May.
    9. Candeal-Haro, Juan Carlos & Indurain-Eraso, Esteban, 1993. "Utility representations from the concept of measure," Mathematical Social Sciences, Elsevier, vol. 26(1), pages 51-62, July.
    10. Mehta, Ghanshyam B., 1995. "Metric utility functions," Journal of Economic Behavior & Organization, Elsevier, vol. 26(2), pages 289-298, March.
    11. Beardon, Alan F & Mehta, Ghanshyam B, 1994. "The Utility Theorems of Wold, Debreu, and Arrow-Hahn," Econometrica, Econometric Society, vol. 62(1), pages 181-186, January.
    12. Mehta, Ghanshyam, 1985. "Continuous utility functions," Economics Letters, Elsevier, vol. 18(2-3), pages 113-115.
    13. Beardon, Alan F. & Candeal, Juan C. & Herden, Gerhard & Indurain, Esteban & Mehta, Ghanshyam B., 2002. "The non-existence of a utility function and the structure of non-representable preference relations," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 17-38, February.
    14. Mehta, Ghanshyam, 1981. "A New Extension Procedure for the Arrow-Hahn Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(1), pages 113-118, February.
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    Cited by:

    1. Gori, Michele & Pianigiani, Giulio, 2010. "On the Arrow-Hahn utility representation method," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 282-287, May.

    More about this item


    Utility function Banach space;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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