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On the continuity of the Young-Fenchel transform. (English) Zbl 0253.46086


MSC:

46E99 Linear function spaces and their duals
46B10 Duality and reflexivity in normed linear and Banach spaces
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References:

[1] Brøndsted, A., Conjugate convex functions in topological vector spaces, Mat.-Fys. Medd. Danske Vid. Selsk., 34 (1964) · Zbl 0119.10004
[2] Fenchel, W., On conjugate convex functions, Canad. J. Math., 1, 73-77 (1949) · Zbl 0038.20902
[3] Fenchel, W., Convex cones, sets and functions, (mimeographed notes (1953), Princeton Univ. Press: Princeton Univ. Press Princeton, N. J) · Zbl 0053.12203
[4] Kuratowski, C., Topologie, Vol. 1 (1948), Wroclaw, Warszawa
[5] Ioffe, A.; Tikhomirov, V., Dvoistvennost vuipuchlich funkzji i ekstrémalnie zadaci, Uspechi Mat. Nauk., 23, 51-116 (1968) · Zbl 0167.42202
[6] Moreau, J. J., Fonctions convexes en dualité, (multigraph), (Faculté des Sciences de Montpellier, Séminaire de Mathématique (1962))
[7] Moreau, J. J., Fonctionelles convexes, (Séminaire sur les équations aux dérivées partielles (1966-1967), Collège de France: Collège de France Paris) · Zbl 0343.49021
[8] Mosco, U., Convergence of convex sets and of solutions of variational inequalities, Advances Math., 3, 510-585 (1969) · Zbl 0192.49101
[9] Mosco, U., Perturbation of variational inequalities, (Proc. AMS Symp. on Non-linear Functional Analysis. Proc. AMS Symp. on Non-linear Functional Analysis, Chicago (1968)) · Zbl 0211.17203
[10] Rockafellar, R. T., Extension of Fenchel’s duality theorem for convex functions, Duke Math. J., 33, 81-90 (1966) · Zbl 0138.09301
[11] Rockafellar, R. T., Level sets and continuity of conjugate convex functions, Trans. Amer. Math. Soc., 123, 46-63 (1966) · Zbl 0145.15802
[12] Wijsman, R. A., Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc., 70, 186-188 (1964) · Zbl 0121.39001
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