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2011 | 25 | 27--44
Tytuł artykułu

Fixed Point Approach to the Stability of an Integral Equation in the Sense of Ulam-Hyers-Rassias

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, by using the classical Banach contraction principle, we investigate and establish the stability in the sense of Ulam-Hyers and in the sense of Ulam-Hyers-Rassias for the integral equation which defines the mild solutions of an abstract Cauchy problem in Banach spaces. (original abstract)
Rocznik
Tom
25
Strony
27--44
Opis fizyczny
Twórcy
  • Cadi Ayyad University, Morocco
  • Cadi Ayyad University, Morocco
  • Cadi Ayyad University, Morocco
Bibliografia
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  • Hyers D.H., The stability of homomorphisms and related topics, Global gnalysis-analysis on manifolds (T.M. Rassias ed.), Teubner-Texte Math., B. 57, Teubner, Leipzig, 1983, pp. 140-153.
  • Hyers D.H., Isac G., Rassias Th.M., Stability of Functional Equation in Several Variables, Birkhäuser, Basel, 1998.
  • Jung S.-M., Hyers-Ulam-Rassias stability of Jensen's equation and its application, Proc. Amer. Math. Soc. 126 (1998), 3137-3143.
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  • Miura T., Miyajima S., Takahasi S.-E., Hyers-Ulam stability of linear differential operator with constant coefficients, Math. Nachr. 258 (2003), 90-96.
  • Obloza M., Hyers stability of the linear differential equation, Rocznik Nauk.-Dydakt. Prace Mat. 13 (1993), 259-270.
  • Obloza M., Connections between Hyers and Lyapunov stability of the ordinary differential equations, Rocznik Nauk.-Dydakt. Prace Mat. 14 (1997), 141-146.
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  • Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
  • Radu V., The fixed point alternative and the stability of functional equations, Fixed Point Theory 4 (2003), no. 1, 91-96.
  • Rassias Th.M., On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
  • Rassias Th.M., The problem of S. M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl. 246 (2000), 352-378.
  • Rassias Th.M., On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), 264-284.
  • Rassias Th.M., On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), 23-130.
  • Rassias Th.M., Functional Equations, Inequalities and Applications, Kluwer Academic, Dordrecht, Boston and London, 2003.
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  • Rus I.A., Ulam stabilities of ordinary differential equations in a Banach space, Carpathian J. Math. 26 (2010), no. 1, 103-107.
  • Takahasi S.-E., Miura T., Miyajima S., On the Hyers-Ulam stability of the Banach space valued differential equation $y' = lambda y$, Bull. Korean Math. Soc. 39 (2002), no. 2, 309-315.
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  • Wang J., Some further generalizations of the Hyers-Ulam Rassias stability of functional equations, J. Math. Anal. Appl. 263 (2001), 406-423.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171621632

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