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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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Convergence of asymptotic directions
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by Dinh The Luc and Jean-Paul Penot PDF
Trans. Amer. Math. Soc. 353 (2001), 4095-4121 Request permission

Abstract:

We study convergence properties of asymptotic directions of unbounded sets in normed spaces. The links between the continuity of a set-valued map and the convergence of asymptotic directions are examined. The results are applied to investigate continuity properties of marginal functions and asymptotic directions of level sets.
References
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Additional Information
  • Dinh The Luc
  • Affiliation: Département de Mathematiques, Université d’Avignon, Avignon, France; Hanoi Institute of Mathematics, Hanoi, Vietnam
  • Email: dtluc@univ-avignon.fr
  • Jean-Paul Penot
  • Affiliation: Département de Mathématiques, Université de Pau, Pau, France
  • Email: Jean-Paul.Penot@univ-pau.fr
  • Received by editor(s): December 27, 1994
  • Received by editor(s) in revised form: December 27, 1999
  • Published electronically: May 17, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 4095-4121
  • MSC (1991): Primary 54A20
  • DOI: https://doi.org/10.1090/S0002-9947-01-02664-2
  • MathSciNet review: 1837222