Optimization Letters

, Volume 8, Issue 1, pp 237–246 | Cite as

Some results on the convexity of the closure of the domain of a maximally monotone operator

  • Jonathan M. Borwein
  • Liangjin YaoEmail author
Original Paper


We provide a concise analysis about what is known regarding when the closure of the domain of a maximally monotone operator on an arbitrary real Banach space is convex. In doing so, we also provide an affirmative answer to a problem posed by Simons.


Nearly convex set Fitzpatrick function Maximally monotone operator Monotone operator Set-valued operator 

Mathematics Subject Classification (2010)

Primary 47H05 Secondary 26B25 47A05 47B65 



The authors thank an anonymous referee for his/her pertinent comments. Jonathan Borwein and Liangjin Yao were both partially supported by the Australian Research Council.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.CARMA, University of NewcastleNewcastleAustralia

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