Abstract
Answering a question of L. Reich, we here present two results about the behavior of functions satisfying the approximate additivity inequality almost everywhere with respect to an axiomatically given family of “small” (“negligible”) sets.
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References
J.A. Baker, J. Lawrence, and F. Zorzitto, The stability of the equation f(x + y) = f(x)f(y). Proc. Amer. Math. Soc. 74 (1979), 242–246.
N.G. de Bruijn, On almost additive functions. Colloq. Math. 15 (1966), 59–63.
P. Cholewa, The stability problem for a generalized Cauchy type functional equation. Rev. Roumaine Math. Pures Appl. (to appear).
J.G. Dhombres, Some Aspects of Functional Equations. Chulalongkorn University Press, Bangkok, 1979.
J.G. Dhombres and R. Ger, Conditional Cauchy equations. Glasnik Mat. 13 (33) (1978), 39–62.
P. Erdös, P 310. Colloq. Math. 7 (1960), 311.
G.L. Forti, An existence and stability theorem for a class of functional equations (to appear).
R. Ger, On sane functional equations with a restricted domain, I, II. Fund. Math. 89 (1975), 131–149.
R. Ger, On sane functional equations with a restricted domain, I, II. Fund. Math. 98 (1978), 249–272.
R. Ger, Almost additive functions on semigroups and a functional equation. Publ. Math. Debrecen 26 (1979, 219–228.
S. Hartman, A remark about Cauchy’s equation. Colloq. Math. 18 (1961), 77–79.
D.H. Hyers, On the stability of the linear functional equation. Proc. Nat. Acad. Sci. USA 27 (1941), 222–224.
W.B. Jurkat, On Cauchy’s functional equation. Proc. Amer. Math. Soc. 16 (1965), 683–686.
M. Kuczma, Functional equations on restricted domains. Aequationes Math. 18 (1978), 1–34.
G. Pólya and G. Szegö, Problems and Theorems in Analysis I. Springer Verlag, New York-Heidelberg-Berlin, 1972 (Chapter 3, §1, Problem 99); first edition: 1925 (in German).
J. Rätz, On approximately additive mappings, pp. 233–251 in Proceedings of the Second International Conference on General Inequalities, ISNM vol. 47, edited by E.F. Beckenbach. Birkhauser Verlag, Basel-Boston-Stuttgart, 1980.
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Ger, R. (1983). Almost Approximately Additive Mappings. In: Beckenbach, E.F., Walter, W. (eds) General Inequalities 3. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 64. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6290-5_20
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DOI: https://doi.org/10.1007/978-3-0348-6290-5_20
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-6292-9
Online ISBN: 978-3-0348-6290-5
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