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Proceedings of the American Mathematical Society

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On the asymptoticity aspect
of Hyers-Ulam stability of mappings

Authors: D. H. Hyers, G. Isac and Th. M. Rassias
Journal: Proc. Amer. Math. Soc. 126 (1998), 425-430
MSC (1991): Primary 39B72, 47H15
MathSciNet review: 1415589
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Abstract: The object of the present paper is to prove an asymptotic analogue of Th.M. Rassias' theorem obtained in 1978 for the Hyers-Ulam stability of mappings.

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D. H. Hyers
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-1113

G. Isac
Affiliation: Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Ontario, Canada K7K 5L0

Th. M. Rassias
Affiliation: Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece

Keywords: Hyers-Ulam stability, asymptotic conditions, asymptotically derivable, additive outside a ball
Received by editor(s): December 11, 1995
Received by editor(s) in revised form: May 21, 1996, and July 29, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society