Trang, Nguyen Thi Quynh A note on an approximate mean value theorem for Fréchet subgradients. (English) Zbl 1238.49021 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 1, 380-383 (2012). Summary: We derive a new characterization of Asplund spaces and give a clarification of the proof of the approximate mean value theorem in B. S. Mordukhovich [Variational analysis and generalized differentiation. I: Basic theory. II: Applications, Grundlehren der Mathematischen Wissenschaften 331/332. Berlin: Springer (ISBN 3-540-25437-4/hbk; 3-540-25438-2/hbk). xxii, 579 p./v.1, xxii, 610 p. (2006; Zbl 1100.49002]] and B.S. Mordukhovich and Y. Shao [”Extremal characterizations of Asplund spaces”, Proc. Am. Math. Soc. 124, No.1, 197-205 (1996; Zbl 0849.46010)]. Cited in 1 Document MSC: 49J40 Variational inequalities 49J45 Methods involving semicontinuity and convergence; relaxation 49J52 Nonsmooth analysis Keywords:Asplund spaces; approximation mean value theorem; characterization Citations:Zbl 1100.49002; Zbl 0849.46010 PDFBibTeX XMLCite \textit{N. T. Q. Trang}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 1, 380--383 (2012; Zbl 1238.49021) Full Text: DOI References: [1] Mordukhovich, B. S.; Shao, Y., Nonsmooth sequential analysis in Asplund spaces, Trans. Amer. Math. Soc., 124, 1235-1280 (1996) · Zbl 0881.49009 [2] Loewen, P. D., A mean value theorem for Fréchet subgradients, Nonlinear Anal., 23, 1365-1381 (1994) · Zbl 0824.46047 [3] Thibault, L., A note on the Zagrodny mean value theorem, Optimization, 35, 127-130 (1995) · Zbl 0837.49012 [4] Zagrodny, D., Approximate mean value theorem for upper subderivatives, Nonlinear Anal., 12, 1413-1428 (1988) · Zbl 0689.49017 [5] Mordukhovich, B. S., Variational Analysis and Generalized Differentiation, Vol. I: Basic Theory (2006), Springer: Springer Berlin [6] Mordukhovich, B. S.; Nam, N. M.; Yen, N. D., Fréchet subdifferential calculus and optimality conditions in mathematical programming, Optimization, 55, 685-708 (2006) · Zbl 1121.49017 [7] Fabian, M., Gâteaux Differentiability of Convex Functions and Topology. Weak Asplund Spaces (1997), Wiley: Wiley New York · Zbl 0883.46011 [8] Mordukhovich, B. S.; Shao, Y., Extremal characterizations of Asplund spaces, Proc. Amer. Math. Soc., 124, 197-205 (1996) · Zbl 0849.46010 [9] Phelps, R. R., Convex Functions, Monotone Operators and Differentiability (1993), Springer: Springer Berlin · Zbl 0921.46039 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.