Bulletin of the Iranian Mathematical Society

, Volume 44, Issue 5, pp 1283–1294 | Cite as

\(\varepsilon \)-Subdifferential as an Enlargement of the Subdifferential

  • Mahboubeh Rezaie
  • Zahra Sadat MirsaneyEmail author
Original Paper


This work introduces a remarkable property of enlargements of maximal monotone operators. The basic tool in our analysis is a family of enlargements, introduced by Svaiter. Using the fact that the \(\varepsilon \)-subdifferential operator can be regarded as an enlargement of the subdifferential, a sufficient condition for some calculus rules in convex analysis can be provided. We give several corollaries about \(\varepsilon \)-subdifferential and extend one of them to arbitrary enlargement.


Subdifferential \(\varepsilon \)-Subdifferential Enlargement \(\hbox {Weak}^{*}\)-lower semicontinuity 

Mathematics Subject Classification

Primary 47H05 Secondary 47H04 26E25 47N10 



The authors would like to thank the referees for valuable suggestions and remarks. We thank Professor R. S. Burachik who provided insight and expertise that greatly assisted the research.


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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  1. 1.Department of SciencesUniversity of IsfahanIsfahanIran

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