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Subdifferentials are locally maximal monotone

Published online by Cambridge University Press:  17 April 2009

S. Simons
S. Simons
Affiliation:
Department of Mathematics, University of California, Santa Barbara CA 93106–3080, United States of America
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In a recent paper, Fitzpatrick and Phelps introduced a new class of operators on a Banach space, the locally maximal monotone operators, and showed that this kind of operator can be approximated by a sequence of nicer maximal monotone operators. We give here an affirmative answer to a question posed in this paper: is the subdifferential of a proper convex lower semicontinuous function necessarily locally maximal monotone? Since a locally maximal operator is maximal monotone, our result represents a strengthening of Rockafellar's maximal monotonicity theorem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 3 , June 1993 , pp. 465 - 471
Copyright
Copyright © Australian Mathematical Society 1993

References

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