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A Note on the Stability of an Integral Equation

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Functional Equations in Mathematical Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 52))

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.

Mathematics Subject Classification (2000): Primary 34K20; Secondary 26D10

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Authors and Affiliations

  1. Department of Applied Mathematics and Physics, Graduate School of Science and Engineering, Yamagata University, Yonezawa, 992-8510, Japan

    Takeshi Miura & Sin-Ei Takahasi

  2. Faculty of Engineering, Ibaraki University, Hitachi, 316-8511, Japan

    Go Hirasawa

  3. Department of Informatics, Graduate School of Science and Engineering, Yamagata University, Yonezawa, 992-8510, Japan

    Takahiro Hayata

Authors
  1. Takeshi Miura
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  2. Go Hirasawa
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  3. Sin-Ei Takahasi
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  4. Takahiro Hayata
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Corresponding author

Correspondence to Takeshi Miura .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, National Technical University of Athens, Iroon Polytechneiou 9, Athens, 15780, Greece

    Themistocles M. Rassias

  2. Institute of Mathematics, Pedagogical University, ul. Podchorazych 2, Krakow, 30-084, Poland

    Janusz Brzdek

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Miura, T., Hirasawa, G., Takahasi, SE., Hayata, T. (2011). A Note on the Stability of an Integral Equation. In: Rassias, T., Brzdek, J. (eds) Functional Equations in Mathematical Analysis. Springer Optimization and Its Applications(), vol 52. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0055-4_17

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