This is a preview of subscription content, log in via an institution to check access.
References
E. Asplund andR. T. Rockafellar, Gradients of convex functions. Trans. Amer. Math. Soc.139, 443–467 (1969).
H.Attouch, Variational convergence for functions and operators. London-Boston 1984.
G. Beer, On Mosco convergence of convex sets. Bull. Austral. Math. Soc.38, 239–253 (1988).
G. Beer, On the Young-Fenchel transform for convex functions. Proc. Amer. Math. Soc.104, 1115–1123 (1988).
G.Beer and V. D.Pai, On convergence of convex sets and relative Chebyshev centers. To appear, J. Approx. Theory.
J.Giles, Convex analysis with application in differentiation of convex functions. Res. Notes in Math.58, London 1982.
R.Holmes, A course in optimization and best approximation. LNM257, Berlin-Heidelberg-New York 1972.
J. Joly, Une famille de topologies sur l'ensemble des fonctions convexes pour lesquelles la polarité est bicontinue. J. Math. Pures Appl.52, 421–441 (1973).
E.Klein and A.Thompson, Theory of correspondences. New York-London-Toronto 1984.
R. Lucchetti, Some aspects of the connections between Hadamard and Tyhonov well-posed-ness of convex programs. Boll. Un. Mat. Ital., Analisi Funz. e Appl.1, 337–345 (1982).
L. Mclinden, Successive approximation and linear stability involving convergent sequences of optimization problems. J. Approx. Theory35, 311–354 (1982).
E. Michael, Selected selection theorems. Amer. Math. Monthly63, 233–238 (1956).
U. Mosco, Convergence of convex sets and of solutions of variational inequalities. Adv. in Math.3, 510–585 (1969).
U. Mosco, On the continuity of the Young-Fenchel transform. J. Math. Anal. Appl.35, 518–535 (1971).
R. T.Rockafellar, Convex analysis. Princeton, N.J. 1970.
G. Sallinetti andR. Wets, On the relationship between two types of convergence for convex functions. J. Math. Anal. Appl.60, 211–226 (1977).
W. Vervaat, Une compactification des espaces fonctionnelsC etD: une alternative pour la démonstration des théoremes limites fonctionnels. CRAS Paris292, 441–444 (1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Beer, G. Three characterizations of the Mosco topology for convex functions. Arch. Math 55, 285–292 (1990). https://doi.org/10.1007/BF01191170
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01191170