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Every maximally monotone operator of Fitzpatrick–Phelps type is actually of dense type

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Abstract

We show that every maximally monotone operator of Fitzpatrick–Phelps type defined on a real Banach space must be of dense type. This provides an affirmative answer to a question posed by Stephen Simons in 2001 and implies that various important notions of monotonicity coincide.

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Authors and Affiliations

  1. Mathematics, Irving K. Barber School, University of British Columbia, Kelowna, BC, V1V 1V7, Canada

    Heinz H. Bauschke, Xianfu Wang & Liangjin Yao

  2. CARMA, University of Newcastle, Newcastle, NSW, 2308, Australia

    Jonathan M. Borwein

Authors
  1. Heinz H. Bauschke
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  2. Jonathan M. Borwein
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  3. Xianfu Wang
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  4. Liangjin Yao
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Correspondence to Liangjin Yao.

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Bauschke, H.H., Borwein, J.M., Wang, X. et al. Every maximally monotone operator of Fitzpatrick–Phelps type is actually of dense type. Optim Lett 6, 1875–1881 (2012). https://doi.org/10.1007/s11590-011-0383-2

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  • DOI: https://doi.org/10.1007/s11590-011-0383-2

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