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Abstract Concavity of Increasing Co-radiant and Quasi-Concave Functions with Applications in Mathematical Economics

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  • S. Mirzadeh

    (Shahid Bahonar University of Kerman)

  • H. Mohebi

    (Shahid Bahonar University of Kerman)

Abstract

In this paper, we study nonnegative, increasing, co-radiant and quasi-concave functions over real locally convex topological vector spaces. Such functions have frequently been employed in microeconomic analysis. We next characterize the abstract concavity, the upper support set and the superdifferential of this class of functions by applying a type of duality, which is used in microeconomic theory.

Suggested Citation

  • S. Mirzadeh & H. Mohebi, 2016. "Abstract Concavity of Increasing Co-radiant and Quasi-Concave Functions with Applications in Mathematical Economics," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 443-472, May.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:2:d:10.1007_s10957-016-0901-6
    DOI: 10.1007/s10957-016-0901-6
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    References listed on IDEAS

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    1. Juan Enrique Martínez-Legaz & Alexander M. Rubinov & Siegfried Schaible, 2005. "Increasing quasiconcave co-radiant functions with applications in mathematical economics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(2), pages 261-280, June.
    2. Martinez-Legaz, Juan-Enrique & Santos, Manuel S., 1996. "On expenditure functions," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 143-163.
    3. Jean-Paul Penot & Michel Volle, 1990. "On Quasi-Convex Duality," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 597-625, November.
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