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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Level sets and continuity of conjugate convex functions
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by R. T. Rockafellar PDF
Trans. Amer. Math. Soc. 123 (1966), 46-63 Request permission
References
    N. Bourbaki, Espaces vectoriels topologiques, Chapters III, IV, and V, Hermann, Paris, 1955.
  • Arne Brøndsted, Conjugate convex functions in topological vector spaces, Mat.-Fys. Medd. Danske Vid. Selsk. 34 (1964), no. 2, 27 pp. (1964). MR 166580
  • Gustave Choquet, Ensembles et cônes convexes faiblement complets, C. R. Acad. Sci. Paris 254 (1962), 1908–1910 (French). MR 132373
  • H. G. Eggleston, Convexity, Cambridge Tracts in Mathematics and Mathematical Physics, No. 47, Cambridge University Press, New York, 1958. MR 0124813
  • Ky Fan, A generalization of the Alaoglu-Bourbaki theorem and its applications, Math. Z. 88 (1965), 48–60. MR 178326, DOI 10.1007/BF01112692
  • W. Fenchel, On conjugate convex functions, Canad. J. Math. 1 (1949), 73–77. MR 28365, DOI 10.4153/cjm-1949-007-x
  • —, Convex cones, sets and functions, Lecture notes, mimeograph, Princeton Univ. Princeton, N.J., 1953. L. Hörmander, Sur la fonction d’appui des ensembles convexes, dans une espace localement convexe, Ark. Mat. 3 (1954), 181-186. J. J. Moreau, Fonctions convexes en dualité, (multigraph), Faculté des Sciences, Séminaires de Mathématiques, Université de Monpellier, Montpellier, 1962.
  • Jean-Jacques Moreau, Sur la fonction polaire d’une fonction semi-continue supérieurement, C. R. Acad. Sci. Paris 258 (1964), 1128–1130 (French). MR 160093
  • R. R. Phelps, Extreme points of polar convex sets, Proc. Amer. Math. Soc. 12 (1961), 291–296. MR 121634, DOI 10.1090/S0002-9939-1961-0121634-3
  • R. T. Rockafellar, Convex functions and dual extremum problems, Doctoral dissertation, Harvard University, Cambridge, Mass., 1963.
  • R. T. Rockafellar, Helly’s theorem and minima of convex functions, Duke Math. J. 32 (1965), 381–397. MR 179687
  • R. T. Rockafellar, Extension of Fenchel’s duality theorem for convex functions, Duke Math. J. 33 (1966), 81–89. MR 187062
  • —, Dual extremum problems involving convex functions, Pacific J. Math. (1966) (to appear).
  • J. J. Stoker, Unbounded convex point sets, Amer. J. Math. 62 (1940), 165–179. MR 1029, DOI 10.2307/2371445
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Additional Information
  • © Copyright 1966 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 123 (1966), 46-63
  • MSC: Primary 46.90
  • DOI: https://doi.org/10.1090/S0002-9947-1966-0192318-X
  • MathSciNet review: 0192318