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

 

On the Bartle-Graves theorem


Authors: J. M. Borwein and A. L. Dontchev
Journal: Proc. Amer. Math. Soc. 131 (2003), 2553-2560
MSC (2000): Primary 49J53, 46N10, 47H04, 54C60
Published electronically: March 17, 2003
MathSciNet review: 1974655
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Abstract: The Bartle-Graves theorem extends the Banach open mapping principle to a family of linear and bounded mappings, thus showing that surjectivity of each member of the family is equivalent to the openness of the whole family. In this paper we place this theorem in the perspective of recent concepts and results, and present a general Bartle-Graves theorem for set-valued mappings. As applications, we obtain versions of this theorem for mappings defined by systems of inequalities, and for monotone variational inequalities.


References [Enhancements On Off] (What's this?)

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Additional Information

J. M. Borwein
Affiliation: FRSC, Canada Research Chair in Information Technology, Centre for Experimental and Constructive Mathematics, Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6

A. L. Dontchev
Affiliation: Mathematical Reviews, Ann Arbor, Michigan 48107-8604

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07229-0
PII: S 0002-9939(03)07229-0
Received by editor(s): June 11, 2002
Received by editor(s) in revised form: February 12, 2003
Published electronically: March 17, 2003
Dedicated: Dedicated to Bob Bartle
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2003 American Mathematical Society