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Local boundedness of monotone operators under minimal hypotheses

  • Jon Borwein (a1) and Simon Fitzpatrick (a2)

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

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[1] Borwein, J.M. and Tingley, D.A., ‘On supportless convex sets’, Proc. Amer. Math. Soc. 94 (1985), 471476.
[2] Holmes, R.B., Geometric Functional Analysis and Applications (Springer-Verlag, New York, 1975).
[3] Phelps, R.R., Convex functions, Monotone Operators and Differentiability, Lecture Notes in Mathematics (Springer-Verlag, University of Washington, 1989). (to appear).
[4] Rockafellar, R.T., ‘Local boundedness of nonlinear monotone operators’, Mitchigan Math. J. 16 (1969), 397407.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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