Abstract
We prove a non-stability result for linear recurrences with constant coefficients in Banach spaces. As a consequence we obtain a complete solution of the problem of the Hyers-Ulam stability for those congruences in the complex Banach space.
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R. P. Agarwal, B. Xu, andW. Zhang, Stability of functional equations in single variable.J. Math. Anal. Appl. 288 (2003), 852–869.
C. Borelli andG. L. Forti, On a general Hyers-Ulam stability result.Internat. J. Math. Math. Sci. 18 (1995), 229–236.
D. G. Bourgin, Classes of transformations and bordering transformations.Bull. Am. Math. Soc. 57 (1951), 223–237.
G. L. Forti, An existence and stability theorem for a class of functional equations.Stochastica 4 (1980), 23–30
—, Hyers-Ulam stability of functional equations in several variables.Aequationes Math.50 (1995), 143–190.
R. Ger, A survey of recent results on stability of functional equations. In:Proc. of the 4th International Conference on Functional Equations and Inequalities (Cracow), Pedagogical University of Cracow, Poland, 1994, pp. 5–36.
P. M. Gruber, Stability of isometries.Trans. Amer. Math. Soc. 245 (1978), 263–277.
D. H. Hyers, On the stability of the linear functional equation.Proc. Nat. Acad. Sci. USA 27 (1941), 222–224.
D. H. Hyers, G. Isac, and T. M. Rassias,Stability of Functional Equations in Several Variables. Birkhäuser, 1998.
Z. Moszner, Sur la stabilité de l’équation d’homomorphisme.Aequationes Math. 29 (1985), 290–306.
D. Popa, Hyers-Ulam stability of the linear recurrence with constant coefficients.Adv. Difference Equ. 2005:2 (2005), 101–107.
J. Rätz, On approximately additive mappings. In:General inequalities 2 (Proc. Second Internat. Conf., Oberwolfach, 1978), Birkhäuser, Basel-Boston, Mass., 1980, pp. 233–251.
S. M. Ulam,Problems in Modern Mathematics, Science Editions. John-Wiley & Sons Inc., New York, 1964.
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Communicated by: A. Kreuzer
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Brzdk, J., Popa, D. & Xu, B. Note on nonstability of the linear recurrence. Abh.Math.Semin.Univ.Hambg. 76, 183–189 (2006). https://doi.org/10.1007/BF02960864
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DOI: https://doi.org/10.1007/BF02960864