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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 13, Issue 1


Volume 13 (2015)

On the use of semi-closed sets and functions in convex analysis

Constantin Zălinescu
  • Corresponding author
  • Faculty of Mathematics, University Alexandru Ioan Cuza, Iaşi, Romania/ Octav Mayer Institute of Mathematics, Romanian Academy, Iaşi, Romania
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Published Online: 2014-10-09 | DOI: https://doi.org/10.1515/math-2015-0001


The main aim of this short note is to show that the subdifferentiability and duality results established by Laghdir (2005), Laghdir and Benabbou (2007), and Alimohammady et al. (2011), stated in Fréchet spaces, are consequences of the corresponding known results using Moreau-Rockafellar type conditions.

Keywords : Semi-closed convex set; Semi-closed convex function; Semi-closure; Semi-interior; Subdifferential; Duality


  • [1] Alimohammady, M., Cho, Y.J., Dadashi, V., Roohi, M., Convex sub-differential sum rule via convex semi-closed functions with applications in convex programming, Appl. Math. Lett., 2011, 24(8), 1289-1294CrossrefGoogle Scholar

  • [2] Laghdir, M., Some remarks on subdifferentiability of convex functions, Appl. Math. E-Notes, 2005, 5, 150-156 (electronic)Google Scholar

  • [3] Laghdir, M., Benabbou, R., Convex functions whose epigraphs are semi-closed: duality theory, Appl. Math. Sci. (Ruse), 2007, 1(21-24), 1019-1033Google Scholar

  • [4] Zălinescu, C., Convex Analysis in General Vector Spaces, World Scientific, River Edge, 2002Google Scholar

  • [5] Zălinescu, C., Hahn-Banach extension theorems for multifunctions revisited, Math. Methods Oper. Res., 2008, 68(3), 493-508Web of ScienceGoogle Scholar

About the article

Received: 2013-08-24

Accepted: 2014-03-19

Published Online: 2014-10-09

Published in Print: 2015-01-01

Citation Information: Open Mathematics, Volume 13, Issue 1, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0001.

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© 2015 Constantin Zălinescu. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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