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Hyers-Ulam stability of linear differential equations of first order. II. (English) Zbl 1125.34328
Summary: Let \(X\) be a complex Banach space and let \(I\) be an open interval. For given functions \(g : I \rightarrow \mathbb C,\;h : I \rightarrow X\) and \(\varphi : I \rightarrow [0,\infty )\), we will solve the differential inequality \(\| y^{\prime}(t) + g(t)y(t)+h(t)\| \leq \varphi (t)\) for the class of continuously differentiable functions \(y : I \rightarrow X\) under some integrability conditions.
Part I, cf. Appl. Math. Lett. 17, No. 10, 1135–1140 (2004; Zbl 1061.34039); Part III, cf. J. Math. Anal. Appl. 311, No. 1, 139–146 (2005; Zbl 1087.34534).

MSC:
34G10 Linear differential equations in abstract spaces
34A40 Differential inequalities involving functions of a single real variable
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[1] Hyers, D.H.; Isac, G.; Rassias, Th.M., Stability of functional equations in several variables, (1998), Birkhäuser Boston · Zbl 0894.39012
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[4] Takahasi, S.-E.; Miura, T.; Miyajima, S., On the hyers – ulam stability of the Banach space-valued differential equation \(y^\prime = \lambda y\), Bull. Korean math. soc., 39, 309-315, (2002) · Zbl 1011.34046
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[7] Jung, S.-M., Hyers – ulam stability of linear differential equations of first order, Appl. math. lett., 17, 1135-1140, (2004) · Zbl 1061.34039
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