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Local boundedness of monotone operators under minimal hypotheses

Published online by Cambridge University Press:  17 April 2009

Jon Borwein  and
Simon Fitzpatrick
Jon Borwein
Affiliation:
Department of Mathematics Statistics and Computer Science, Dalhousie University, Halifax NS B3H 3J5Canada
Simon Fitzpatrick
Affiliation:
Department of Mathematics and Statistics, University of Auckland, Private BagAucklandNew Zealand
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Abstract

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We give a short proof the local boundedness of a monotone operator as an easy consequence of the continuity of an associated convex function.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 3 , June 1989 , pp. 439 - 441
Copyright
Copyright © Australian Mathematical Society 1989

References

[1] Borwein, J.M. and Tingley, D.A., ‘On supportless convex sets’, Proc. Amer. Math. Soc. 94 (1985), 471–476.CrossRefGoogle Scholar
[2] Holmes, R.B., Geometric Functional Analysis and Applications (Springer-Verlag, New York, 1975).CrossRefGoogle Scholar
[3] Phelps, R.R., Convex functions, Monotone Operators and Differentiability, Lecture Notes in Mathematics (Springer-Verlag, University of Washington, 1989). (to appear).CrossRefGoogle Scholar
[4] Rockafellar, R.T., ‘Local boundedness of nonlinear monotone operators’, Mitchigan Math. J. 16 (1969), 397–407.Google Scholar