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

No 21/2004, Memorandum from Oslo University, Department of Economics

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 (search for similar items in EconPapers)
JEL-codes: F41 (search for similar items in EconPapers)
Pages: 13 pages
Date: 2004-10-28
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Persistent link: https://EconPapers.repec.org/RePEc:hhs:osloec:2004_021

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