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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Differentiability and regularity of Lipschitzian mappings


Authors: Boris S. Mordukhovich and Bingwu Wang
Journal: Proc. Amer. Math. Soc. 131 (2003), 389-399
MSC (2000): Primary 49J52; Secondary 58C20
Published electronically: September 25, 2002
MathSciNet review: 1933329
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Abstract: We introduce new differentiability properties of functions between Banach spaces and establish their relationships with graphical regularity of Lipschitzian single-valued and set-valued mappings. The proofs are based on advanced tools of nonsmooth variational analysis including new results on coderivative scalarization and normal cone calculus.


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Additional Information

Boris S. Mordukhovich
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email: boris@math.wayne.edu

Bingwu Wang
Affiliation: Department of Mathematics, Eastern Michigan University, Ypsilanti, Michigan 48197
Email: wangbw@math.emich.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06836-3
PII: S 0002-9939(02)06836-3
Keywords: Lipschitzian mappings, differentiability, Banach spaces, variational analysis, graphical regularity
Received by editor(s): March 23, 2001
Published electronically: September 25, 2002
Additional Notes: The first author was partly supported by the National Science Foundation under grants DMS-9704751 and DMS-0072179 and also by the Distinguished Faculty Fellowship at Wayne State University.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2002 American Mathematical Society