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On the stability of approximately additive mappings

Author(s): Yang-Hi Lee; Kil-Woung Jun
Journal: Proc. Amer. Math. Soc. 128 (2000), 1361-1369.
MSC (1991): Primary 47H15
Posted: August 5, 1999
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Abstract: In this paper we prove a generalization of the stability of approximately additive mappings in the spirit of Hyers, Ulam and Rassias.

References:

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Z. Gajda, On stability of additive mappings, Internat. J. Math. Sci 14 (1991), 431-434.MR 92e:39029

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D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222-224.MR 2:315a

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G. Isac and Th. M. Rassias, On the Hyers-Ulam stability of $\psi $-additive mappings, J. Approx. Theory 72 (1993), 131-137. MR 94b:39043

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G. Isac and Th. M. Rassias, Functional inequalities for approximately additive mappings, In: Stability of Mappings of Hyers-Ulam Type (Th. M. Rassias and J. Tabor, eds.), Hadronic Press, Palm Harbor, Fl. (1994), 117-125.MR 95j:39048

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Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.MR 80d:47094

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Th. M. Rassias and P. [??]Semrl, On the behavior of mappings which does not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc. 114 (1992), 989-993.MR 92g:47101

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Additional Information:

Yang-Hi Lee
Affiliation: Department of Mathematics Education, Kongju National University of Education, Kongju 314-060, Republic of Korea
Email: lyhmzi@kongjuw2.kongju-e.ac.kr

Kil-Woung Jun
Affiliation: Department of Mathematics, Chungnam National University, Taejon 305-764, Republic of Korea
Email: kwjun@math.chungnam.ac.kr

DOI: 10.1090/S0002-9939-99-05156-4
PII: S 0002-9939(99)05156-4
Received by editor(s): February 25, 1998
Received by editor(s) in revised form: June 22, 1998
Posted: August 5, 1999
Communicated by: Dale Alspach
Copyright of article: Copyright 2000, American Mathematical Society

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Yang-Hi Lee and Kil-Woung Jun, A Generalization of the Hyers-Ulam-Rassias Stability of Jensen's Equation, Journal of the Mathematical Analysis and Applicatons 238 (1999), 305-315.

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