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A fixed-point theorem for asymptotically contractive mappings

Author: Jean-Paul Penot
Journal: Proc. Amer. Math. Soc. 131 (2003), 2371-2377
MSC (2000): Primary 47H10, 47H09, 54H25, 55M20
Published electronically: March 11, 2003
MathSciNet review: 1974633
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Abstract: We present fixed point theorems for a nonexpansive mapping from a closed convex subset of a uniformly convex Banach space into itself under some asymptotic contraction assumptions. They generalize results valid for bounded convex sets or asymptotically compact sets.

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Additional Information

Jean-Paul Penot
Affiliation: Laboratoire de Mathématiques Appliquées, CNRS F.R.E. 2570, Faculté des Sciences, av. de l’Université, 64000 Pau, France

Keywords: Asymptotic, asymptotic cone, contraction, derivative at infinity, firm asymptotic cone, fixed point, nonexpansive map
Received by editor(s): February 19, 2002
Published electronically: March 11, 2003
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2003 American Mathematical Society

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