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Hyers–Ulam Stability of First Order Differential Equation via Integral Inequality

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Abstract

In this chapter, first we derive a nonlinear integral inequality of Gollwitzer type, and as an application we investigate the Hyers–Ulam stability of nonlinear differential equation

$$\displaystyle y'(t) =f(t,y(t)),\, t\ge a , $$

where f is a given function. The obtained results are new to the literature.

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References

  1. C. Alsina, A. Ger, On some inequalities and stability results related to the exponential function. J. Inequal. Appl. 2, 373–380 (1998)

    MathSciNet  MATH  Google Scholar 

  2. H.E. Gollwitzer, A note on functional inequality. Proc. Am. Math. Soc. 23, 642–647 (1969)

    Article  MathSciNet  Google Scholar 

  3. G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities (Cambridge University Press, Cambridge, 1934)

    MATH  Google Scholar 

  4. Y. Hi, Y. Shen, Hyers-Ulam stability of linear differential equations of second order. Appl. Math. Lett. 23, 306–309 (2010)

    Article  MathSciNet  Google Scholar 

  5. S.M. Jung, Hyers-Ulam stability of linear differential equations of first order. Appl. Math. Lett. 17,1135–1140 (2004)

    Article  MathSciNet  Google Scholar 

  6. S.M. Jung, Hyers-Ulam stability of linear differential equations of first order-III. J. Math. Appl. 311, 139–146 (2005)

    MathSciNet  MATH  Google Scholar 

  7. S.M. Jung, Hyers-Ulam stability of linear differential equations of first order-II. Appl. Math. Lett. 19, 854–858 (2006)

    Article  MathSciNet  Google Scholar 

  8. B.G. Pachpatte, Inequalities for Differential and Integral Equations (Academic Press, New York, 1998)

    MATH  Google Scholar 

  9. J.M. Rassias, Solution of a problem of Ulam. J. Approx. Theory 57, 268–273 (1989)

    Article  MathSciNet  Google Scholar 

  10. J.M. Rassias, E. Thandapani, K. Ravi, B.V. Senthilkumar, Functional Equations and Inequalities: Solutions and Stability Results. Series on Concrete and applicable mathematics (World Scientific Publishing Co. Pte. Ltd., Singapore, 2017)

    Google Scholar 

  11. K. Ravi, M. Arunkumar, J.M. Rassias, Ulam stability for the orthogonally general Euler-Lagrange type functional equation. Int. J. Math. Stat. 3, 36–46 (2008)

    MathSciNet  MATH  Google Scholar 

  12. G. Wang, M. Zhou, L. Sun, Hyers-Ulam stability of linear differential equations of first order. Appl. Math. Lett. 21, 1024–1028 (2008)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, India

    S. Tamilvanan

  2. Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India

    E. Thandapani

  3. Pedagogical Department E.E., Section of Mathematics and Informatics, National and Kapodistrian University of Athens, Athens, Greece

    J. M. Rassias

Authors
  1. S. Tamilvanan
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  2. E. Thandapani
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  3. J. M. Rassias
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Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA

    George A. Anastassiou

  2. Pedagogical Department E. E., Section of Mathematics and Informatics, National and Kapodistrian University of Athens, Athens, Greece

    John Michael Rassias

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Tamilvanan, S., Thandapani, E., Rassias, J.M. (2019). Hyers–Ulam Stability of First Order Differential Equation via Integral Inequality. In: Anastassiou, G., Rassias, J. (eds) Frontiers in Functional Equations and Analytic Inequalities. Springer, Cham. https://doi.org/10.1007/978-3-030-28950-8_9

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