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An approximation property of exponential functions
- Authors
- Jung, S. -M.
- Issue Date
- Jul-2009
- Publisher
- SPRINGER
- Keywords
- linear first order differential equation; power series method; exponential function; approximation; Hyers-Ulam stability; local Hyers-Ulam stability
- Citation
- ACTA MATHEMATICA HUNGARICA, v.124, no.1-2, pp.155 - 163
- Journal Title
- ACTA MATHEMATICA HUNGARICA
- Volume
- 124
- Number
- 1-2
- Start Page
- 155
- End Page
- 163
- ISSN
- 0236-5294
- Abstract
- We solve the inhomogeneous linear first order differential equations of the form y'(x) - lambda y(x) = I pound (m=0) (a) a (m) (x - c) (m) , and prove an approximation property of exponential functions. More precisely, we prove the local Hyers-Ulam stability of linear first order differential equations of the form y'(x) = lambda y(x) in a special class of analytic functions.
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