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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 (Jan 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
  • Email:
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), 1289-1294 [Crossref]

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

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

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

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

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, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0001. Export Citation

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

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