A Note on the Stability of an Integral Equation

Takeshi Miura (), Go Hirasawa (), Sin-Ei Takahasi () and Takahiro Hayata ()
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Takeshi Miura: Yamagata University
Go Hirasawa: Ibaraki University
Sin-Ei Takahasi: Yamagata University
Takahiro Hayata: Yamagata University

Chapter Chapter 17 in Functional Equations in Mathematical Analysis, 2011, pp 207-222 from Springer

Abstract: Abstract Let p: ℝ → ℂ be a continuous function. We give a sufficient condition in order that the integral equation $$f(t) = f(0) +{ \int \nolimits \nolimits }_{0}^{\,t}p(s)f(s)\,\mathrm{d}s$$ have the Hyers–Ulam stability. We also prove that if p has no zeros, then the sufficient condition is a necessary condition.

Keywords: Exponential functions; Hyers–Ulam stability; Hyers–Ulam–Rassias stability (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-0055-4_17

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DOI: 10.1007/978-1-4614-0055-4_17

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