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Open mapping theorems for directionally differentiable functions

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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.

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  • Seierstad, Atle, 2004. "Open mapping theorems for directionally differentiable functions," Memorandum 21/2004, Oslo University, Department of Economics.
    • Handle: RePEc:hhs:osloec:2004_021
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    File URL: http://www.sv.uio.no/econ/english/research/unpublished-works/working-papers/pdf-files/2004/Memo-21-2004.pdf
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    Keywords

    Open mapping theorems; Lipschitz; differentiable mappings; differentiable functions;
    All these keywords.

    JEL classification:

    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics

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