Zălinescu, Constantin On the use of semi-closed sets and functions in convex analysis. (English) Zbl 1308.90132 Open Math. 13, 1-5 (2015). Summary: The main aim of this short note is to show that the subdifferentiability and duality results established by M. Laghdir [Appl. Math. E-Notes 5, 150–156 (2005; Zbl 1085.49022)], M. Laghdir and R. Benabbou [Appl. Math. Sci., Ruse 1, No. 21–24, 1019–1033 (2007; Zbl 1200.90138)], and M. Alimohammady et al. [Appl. Math. Lett. 24, No. 8, 1289–1294 (2011; Zbl 1219.26011)], stated in Fréchet spaces, are consequences of the corresponding known results using Moreau-Rockafellar type conditions. MSC: 90C25 Convex programming Keywords:semi-closed convex set; semi-closed convex function; semi-closure; semi-interior; subdifferential; duality Citations:Zbl 1085.49022; Zbl 1200.90138; Zbl 1219.26011 PDFBibTeX XMLCite \textit{C. Zălinescu}, Open Math. 13, 1--5 (2015; Zbl 1308.90132) Full Text: DOI References: [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; · Zbl 1219.26011 [2] Laghdir, M., Some remarks on subdifferentiability of convex functions, Appl. Math. E-Notes, 2005, 5, 150-156 (electronic); · Zbl 1085.49022 [3] Laghdir, M., Benabbou, R., Convex functions whose epigraphs are semi-closed: duality theory, Appl. Math. Sci. (Ruse), 2007, 1(21-24), 1019-1033; · Zbl 1200.90138 [4] Zălinescu, C., Convex Analysis in General Vector Spaces, World Scientific, River Edge, 2002; · Zbl 1023.46003 [5] Zălinescu, C., Hahn-Banach extension theorems for multifunctions revisited, Math. Methods Oper. Res., 2008, 68(3), 493-508; · Zbl 1171.90016 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.