×

The Hyers–Ulam stability constants of first order linear differential operators. (English) Zbl 1074.47022

In this interesting paper, the authors determine the Hyers–Ulam stability constants of linear differential operators of order one.

MSC:

47E05 General theory of ordinary differential operators
39B82 Stability, separation, extension, and related topics for functional equations
34D99 Stability theory for ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

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] Hyers, D. H., On the stability of the linear functional equations, Proc. Nat. Acad. Sci. USA, 27, 222-224 (1941) · Zbl 0061.26403
[3] Miura, T.; Takahasi, S.-E; Choda, H., On the Hyers-Ulam stability of real continuous function valued differentiable map, Tokyo J. Math., 24, 467-478 (2001) · Zbl 1002.39039
[4] Miura, T., On the Hyers-Ulam stability of a differentiable map, Sci. Math. Japan, 55, 17-24 (2002) · Zbl 1025.47041
[5] Miura, T.; Takahasi, S.-E; Miyajima, S., Hyers-Ulam stability of linear differential operator with constant coefficients, Math. Nachr., 258, 90-96 (2003) · Zbl 1039.34054
[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] 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
[8] Ulam, S. M., Problem in Modern Mathematics (1964), Wiley: Wiley New York, Chapter VI · Zbl 0137.24201
[9] Ulam, S. M., Sets, Numbers and Universes, Selected Works, Part III (1974), MIT Press: MIT Press Cambridge, MA
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.