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A Generalization of the Implicit Function Theorems

8 Pages Posted: 2 Dec 2009 Last revised: 12 Sep 2011

Elvio Accinelli

Facultad de Economía de la Universidad Autónoma de San Luís Potosí

Date Written: November 24, 2009

Abstract

In this work we show that it is possible to extend the classical implicit function theorem to mappings defined in a cartesian product of two convex subsets, not necessarily open, included in the cartesian product of two Banach spaces, in to another Banach space. We apply this theorem to show that the excess utility function for an economy with infinitely many commodities is a differentiable mapping.

Keywords: Implicit Function Theorem's, Banach spaces, excess

JEL Classification: C60

Suggested Citation

Accinelli, Elvio, A Generalization of the Implicit Function Theorems (November 24, 2009). Available at SSRN: https://ssrn.com/abstract=1512763 or http://dx.doi.org/10.2139/ssrn.1512763

Elvio Accinelli (Contact Author)

Facultad de Economía de la Universidad Autónoma de San Luís Potosí ( email )

Av. Pintores S/N
San Luis Potosí, San Luis Potosí 78263
Mexico
52444 8131238/120 (Phone)
52444 8131238 (Fax)

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