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Transactions of the American Mathematical Society

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Convergence of asymptotic directions

Authors: Dinh The Luc and Jean-Paul Penot
Journal: Trans. Amer. Math. Soc. 353 (2001), 4095-4121
MSC (1991): Primary 54A20
Published electronically: May 17, 2001
MathSciNet review: 1837222
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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.

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Additional Information

Dinh The Luc
Affiliation: Département de Mathematiques, Université d’Avignon, Avignon, France; Hanoi Institute of Mathematics, Hanoi, Vietnam

Jean-Paul Penot
Affiliation: Département de Mathématiques, Université de Pau, Pau, France

Keywords: Asymptotic cone, cosmic continuity, marginal function, recession cone, recession function, level set, extreme desirability condition
Received by editor(s): December 27, 1994
Received by editor(s) in revised form: December 27, 1999
Published electronically: May 17, 2001
Article copyright: © Copyright 2001 American Mathematical Society