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Implicit Function Theorems for Nondifferentiable Mappings

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Abstract

Sufficient conditions are given for a mapping to be γ-G inverse differentiable. Constrained implicit function theorems for γ-G inverse differentiable mappings are obtained, where the constraint is taken to be either a closed convex cone or a closed subset. A theorem without assuming the γ-G inverse differentiability in a finite-dimensional space is also presented.

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Authors and Affiliations

  1. Research Fellow, School of Electronics and Computer Science, University of Southampton, Southampton, United Kingdom

    W. Bian

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  1. W. Bian
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Communicated by F. A. Potra

The author thanks the referees for valuable suggestions concerning the presentation of this paper. He also thanks Professor J. R. L. Webb and Dr. M. French for help.

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Bian, W. Implicit Function Theorems for Nondifferentiable Mappings. J Optim Theory Appl 129, 277–292 (2006). https://doi.org/10.1007/s10957-006-9056-1

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  • DOI: https://doi.org/10.1007/s10957-006-9056-1

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