Ubiquitous Subdifferentials, r L –density and Maximal Monotonicity

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• 作者：Stephen Simons ; Xianfu Wang
• 关键词：Abstract subdifferential ; Br?ndsted–Rockafellar property ; Multifunction ; Monotonicity ; Monotone polar ; r L –density ; Primary 49J52 ; Secondary 47H04 ; 47H05 ; 65K10
• 刊名：Set-Valued and Variational Analysis
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：23
• 期：4
• 页码：631-642
• 全文大小：231 KB
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• 作者单位：Stephen Simons (1)
  Xianfu Wang (2)
  
  1. Department of Mathematics, University of California, Santa Barbara, CA, 93106, USA
  2. Department of Mathematics, University of British Columbia, Kelowna, BC, V1V 1V7, Canada
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1877-0541

文摘

In this paper, we first investigate an abstract subdifferential for which (using Ekeland’s variational principle) we can prove an analog of the Br?ndsted–Rockafellar property. We introduce the -r _L –density-of a subset of the product of a Banach space with its dual. A closed r _L –dense monotone set is maximally monotone, but we will also consider the case of nonmonotone closed r _L –dense sets. As a special case of our results, we can prove Rockafellar’s result that the subdifferential of a proper convex lower semicontinuous function is maximally monotone. Keywords Abstract subdifferential Br?ndsted–Rockafellar property Multifunction Monotonicity Monotone polar r _L –density