# zbMATH — the first resource for mathematics

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
##### Citations:
Zbl 1087.34534; Zbl 1061.34039
Full Text:
##### References:
 [1] Hyers, D.H.; Isac, G.; Rassias, Th.M., Stability of functional equations in several variables, (1998), Birkhäuser Boston · Zbl 0894.39012 [2] Jung, S.-M., Hyers – ulam – rassias stability of functional equations in mathematical analysis, (2001), Hadronic Press Palm Harbor · Zbl 0980.39024 [3] 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 [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 [5] Miura, T.; Jung, S.-M.; Takahasi, S.-E., Hyers – ulam – rassias stability of the Banach space valued linear differential equations $$y^\prime = \lambda y$$, J. Korean math. soc., 41, 995-1005, (2004) · Zbl 1069.34079 [6] Miura, T.; Miyajima, S.; Takahasi, S.-E., A characterization of hyers – ulam stability of first order linear differential operators, J. math. anal. appl., 286, 136-146, (2003) · Zbl 1045.47037 [7] Jung, S.-M., Hyers – ulam stability of linear differential equations of first order, Appl. math. lett., 17, 1135-1140, (2004) · Zbl 1061.34039
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.