A CONTINUOUS EXTENSION THAT PRESERVES CONCAVITY, MONOTONICITY AND LIPSCHITZ CONTINUITY

Andrés Carvajal

No 1907, Borradores de Economia from Banco de la Republica

Abstract: The following is proven here: let W : X × C −→ R, where X is convex, be a continuous and bounded function such that for each y ∈ C, the function W (·, y) : X −→ R is concave (resp. strongly concave; resp. Lipschitzian with constant M; resp. monotone; resp. strictly monotone) and let Y ⊇ C. If C is compact, then there exists a continuous extension of W , U : X × Y −→ £infX×C W, supX×C W ¤, such that for each y ∈ Y , the function U (·, y) : X −→ R is concave (resp. strongly concave; resp. Lipschitzian with constant My ; resp. monotone; resp. strictly monotone).

Pages: 14
Date: 2003-01-31
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Citations: View citations in EconPapers (2)

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Related works:
Working Paper: A Continuous Extension that preserves Concavity, Monotonicity and Lipschitz Continuity (2004)
Working Paper: A Continuous Extension that Preserves Concavity, Monotonicity and Lipschitz Continuity (2003)
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Persistent link: https://EconPapers.repec.org/RePEc:col:000094:001907

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