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Hyers-Ulam stability of linear differential equations of first order. (English) Zbl 1061.34039

Summary: We prove the Hyers-Ulam stability for linear differential equations of first order of the form \[ \varphi(t)y'(t)=y(t). \]

MSC:

34D99 Stability theory for ordinary differential equations
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References:

[1] Alsina, C.; Ger, R., On some inequalities and stability results related to the exponential function, J. Inequal. Appl., 2, 373-380 (1998) · Zbl 0918.39009
[2] Miura, T.; Takahasi, S.-E.; Choda, H., On the Hyers-Ulam stability of real continuous function valued differentiable map, Tokyo J. Math., 24, 467-476 (2001) · Zbl 1002.39039
[3] Miura, T., On the Hyers-Ulam stability of a differentiable map, Sci. Math. Japon., 55, 17-24 (2002) · Zbl 1025.47041
[4] Ulam, S. M., Problems in Modern Mathematics (1964), Wiley, Chapter VI · Zbl 0137.24201
[5] Hyers, D. H., On the stability of the linear functional equation, (Proc. Nat. Acad. Sci. U.S.A., 27 (1941)), 222-224 · Zbl 0061.26403
[6] Rassias, Th. M., On the stability of the linear mapping in Banach spaces, (Proc. Amer Math. Soc., 72 (1978)), 297-300 · Zbl 0398.47040
[7] Ger, R.; Šemrl, P., The stability of the exponential equation, (Proc. Amer. Math. Soc., 124 (1996)), 779-787 · Zbl 0846.39013
[8] Hyers, D. H.; Isac, G.; Rassias, Th. M., Stability of Functional Equations in Several Variables (1998), Birkhäuser: Birkhäuser New York · Zbl 0894.39012
[9] Hyers, D. H.; Rassias, Th. M., Approximate homomorphisms, Aequationes Math., 44, 125-153 (1992) · Zbl 0806.47056
[10] Rassias, Th. M., On the stability of functional equations and a problem of Ulam, Acta Appl. Math., 62, 23-130 (2000) · Zbl 0981.39014
[11] Takahasi, S.-E.; Miura, T.; Miyajima, S., On the Hyers-Ulam stability of the Banach space-valued differential equation y′ = λy, Bull. Korean Math. Soc., 39, 309-315 (2002) · Zbl 1011.34046
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