Scandinavian Working Papers in Economics

Memorandum,
Oslo University, Department of Economics

No 21/2004: Open mapping theorems for directionally differentiable functions

Atle Seierstad ()
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Atle Seierstad: Dept. of Economics, University of Oslo, Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway

Abstract: Open mapping theorems are proved for directionally differentiable Lipschitz continuous functions. It is indicated that generalizations to nonsmooth functions that are not directionally differentiable are possible. The results in the paper generalize the open mapping theorems for differentiable mappings, and are different from open mapping theorems for nonsmooth functions in the literature, when these are specialized to directionally differentiable functions.

Keywords: Open mapping theorems; Lipschitz; differentiable mappings; differentiable functions

JEL-codes: F41

13 pages, October 28, 2004

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