On the behavior of mappings which do not satisfy Hyers-Ulam stability-Reference-Cited by-同舟云学术

On the behavior of mappings which do not satisfy Hyers-Ulam stability

Published:1992 Issue:4 Volume:114 Page:989-993
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Rassias Themistocles M.,Šemrl Peter

Abstract

We find an example to show when the Hyers-Ulam stability does not occur for approximately linear mappings. We also investigate the behavior of such mappings.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1992-114-04/S0002-9939-1992-1059634-1/S0002-9939-1992-1059634-1.pdf

Reference6 articles.

1. On stability of additive mappings;Gajda, Zbigniew;Internat. J. Math. Math. Sci.,1991

2. On the stability of the linear functional equation;Hyers, D. H.;Proc. Nat. Acad. Sci. U.S.A.,1941

3. On the stability of the linear mapping in Banach spaces;Rassias, Themistocles M.;Proc. Amer. Math. Soc.,1978

4. On a modified Hyers-Ulam sequence;Rassias, Themistocles M.;J. Math. Anal. Appl.,1991

5. Interscience Tracts in Pure and Applied Mathematics, no. 8;Ulam, S. M.,1960

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