A Continuous Extension that Preserves Concavity, Monotonicity and Lipschitz Continuity
AbstractThe following is proven here: let W : X ÃÂ C ââ R, where X is convex, be a continuous and bounded function such that for each y â C, the function W (ÃÂ·, y) : X ââ R is concave (resp. strongly concave; resp. Lipschitzian with constant M; resp. monotone; resp. strictly monotone) and let Y â C. If C is compact, then there exists a continuous extension of W , U : X ÃÂ Y ââ ÃÂ£infXÃÂC W, supXÃÂC W ÃÂ¤, such that for each y â Y , the function U (ÃÂ·, y) : X ââ R is concave (resp. strongly concave; resp. Lipschitzian with constant My ; resp. monotone; resp. strictly monotone).
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Bibliographic InfoPaper provided by Banco de la Republica de Colombia in its series Borradores de Economia with number 230.
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Other versions of this item:
- Andrés Carvajal, 2003. "A Continuous Extension That Preserves Concavity, Monotonicity And Lipschitz Continuity," BORRADORES DE ECONOMIA 001907, BANCO DE LA REPÚBLICA.
- Andrés Carvajal, 2004. "A Continuous Extension that preserves Concavity, Monotonicity and Lipschitz Continuity," Royal Holloway, University of London: Discussion Papers in Economics 04/27, Department of Economics, Royal Holloway University of London, revised Nov 2004.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Howe, Roger, 1987. "Sections and extensions of concave functions," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 53-64, February.
- Andrés Carvajal, 2004.
"Testable Restrictions of General Equilibrium Theory in Exchange Economies with Externalities,"
Royal Holloway, University of London: Discussion Papers in Economics
04/28, Department of Economics, Royal Holloway University of London, revised Nov 2004.
- Andrés Carvajal, . "Testable Restrictions of General Equilibrium Theory in Exchange Economies with Externalities," Borradores de Economia 231, Banco de la Republica de Colombia.
- Andrés Carvajal, 2003. "Testable Restrictions og General Equilibrium Theory in Exchange Economies with Externalities," BORRADORES DE ECONOMIA 003556, BANCO DE LA REPÚBLICA.
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