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Quasidense Monotone Multifunctions

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Abstract

In this paper, we discuss quasidense multifunctions from a Banach space into its dual, and use the two sum theorems proved in a previous paper to give various characterizations of quasidensity, including two fuzzy ones. We investigate the Fitzpatrick extension of such a multifunction. We prove that a closed monotone quasidense multifunction is maximally monotone locally (that is to say, of “type (FPV)”), and strongly maximal. We also prove that a maximally monotone multifunction is quasidense if, and only if, it is locally maximally monotone (that is to say, of “type (FP)”).

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Authors and Affiliations

  1. Department of Mathematics, University of California, Santa Barbara, CA, 93106, USA

    Stephen Simons

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  1. Stephen Simons
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Correspondence to Stephen Simons.

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This paper is dedicated to the memory of Jon Borwein, whose untimely passing has deprived us of his irreplaceable wit and wisdom.

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Simons, S. Quasidense Monotone Multifunctions. Set-Valued Var. Anal 26, 5–26 (2018). https://doi.org/10.1007/s11228-017-0434-7

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  • DOI: https://doi.org/10.1007/s11228-017-0434-7

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