A Continuous Extension that preserves Concavity, Monotonicity and Lipschitz Continuity

Andrés Carvajal

No 04/27, Royal Holloway, University of London: Discussion Papers in Economics from Department of Economics, Royal Holloway University of London

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: 15 pages
Date: 2004-11, Revised 2004-11
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Related works:
Working Paper: A Continuous Extension that Preserves Concavity, Monotonicity and Lipschitz Continuity (2003)
Working Paper: A CONTINUOUS EXTENSION THAT PRESERVES CONCAVITY, MONOTONICITY AND LIPSCHITZ CONTINUITY (2003)
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