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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Continuity of the Fenchel transform of convex functions
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by Kerry Back PDF
Proc. Amer. Math. Soc. 97 (1986), 661-667 Request permission

Abstract:

Given a separated dual system $(E,E’)$, the Fenchel transform determines a pairing of the convex functions on $E$ with the convex functions on $E’$. This operation is shown to have a continuity property. The result implies that the minimum set of a convex function varies in an upper-semicontinuous way with the function’s conjugate. Several convergence concepts for convex functions are discussed. It is shown for each of the two most useful that the Fenchel transform is not a homeomorphism.
References
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 97 (1986), 661-667
  • MSC: Primary 46A55; Secondary 52A07, 90C25
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0845984-5
  • MathSciNet review: 845984