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

DOI:
https://doi.org/10.1090/S0002-9939-03-07229-0

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.

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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:
https://doi.org/10.1090/S0002-9939-03-07229-0

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