Abstract
In this paper we obtain a stability result for the general linear equation in Hyers-Ulam sense.
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References
J. Aczél, Über eine Klasse von Functionalgleichungen, Comment. Math. Helv. 21 (1948), 247–252.
C. Borelli-Forti and G.L. Forti, On a general Hyers-Ulam stability result, Internat. J. Math. Sci. 18 (1995), 229–236.
G.L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), 143–190.
D.H. Hyers, On the stability of the linear functional equation, Proc. Math. Acad. Sci., U.S.A. 27 (1941), 222–224.
M. Kuczma, An introduction to the theory of functional equations and inequalities, PWN — Uniwersytet Ślaski, Warszawa — Kraków — Katowice, 1985.
Zs. Páles, Hyers-Ulam stability of the Cauchy functional equation on square-symmetric groupoids, Publ. Math. Debrecen 4 (2001), 651–666.
Zs. Páles, P. Volkmann and R.D. Luce, Hyers-Ulam stability of functional equations with a square-symmetric operation, Proc. Natl. Acad. Sci. U.S.A. 95 (1998), 12772–12775 (electronic).
D. Popa, Hyers-Ulam-Rassias stability of the general linear equation, Nonlinear Funct. Anal. & Appl. 4 (2002), 581–588.
J. Rätz, On approximately additive mappings, General Inequalities 2 (E.F. Beckenbach, ed.), International Series in Numerical Mathematics 47 Birkhäuser Verlag, Basel-Boston, 1980, 233–251.
S.M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1964.
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© 2008 Birkhäuser Verlag Basel/Switzerland
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Popa, D. (2008). Approximate Solutions of the Linear Equation. In: Bandle, C., Losonczi, L., Gilányi, A., Páles, Z., Plum, M. (eds) Inequalities and Applications. International Series of Numerical Mathematics, vol 157. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-8773-0_29
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DOI: https://doi.org/10.1007/978-3-7643-8773-0_29
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