Hyers–Ulam and Hyers–Ulam–Rassias Stability of First-Order Nonlinear Dynamic Equations

• Alghamdi, Maryam A. ^[1] ; Alharbi, Mymonah ^[1] ; Bohner, Martin ^[2] ; Hamza, Alaa E. ^[1]
  1. [1] University of Jeddah
  2. [2] Missouri S&T
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 2, 2021
• Idioma: inglés
• DOI: 10.1007/s12346-021-00451-3
• Enlaces
  • Texto completo
• Resumen

  • We investigate Hyers–Ulam and Hyers–Ulam–Rassias stability of first-order nonlinear dynamic equations for functions defined on a time scale with values in a Banach space.

• Referencias bibliográficas
  • Alghamdi, M.A., Aljehani, A., Bohner, M., Hamza, A.E.: Hyers–Ulam and Hyers–Ulam–Rassias stability of first-order linear dynamic equations....
  • Alsina, C., Ger, R.: On some inequalities and stability results related to the exponential function. J. Inequal. Appl. 2(4), 373–380 (1998)
  • Anderson, D.R., Gates, B., Heuer, D.: Hyers–Ulam stability of second-order linear dynamic equations on time scales. Commun. Appl. Anal. 16(3),...
  • Andras, S., Meszaros, A.R.: Ulam–Hyers stability of dynamic equations on time scales via Picard operators. Appl. Math. Comput. 219(9), 4853–4864...
  • Bohner, M., Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser Boston Inc., Boston (2001)
  • Bohner, M., Peterson, A.C.: Advances in Dynamic Equations on Time Scales. Birkhäuser Boston Inc., Boston (2003)
  • Ghaemi, M.B., Gordji, M.E., Alizadeh, B., Park, C.: Hyers-Ulam stability of exact second-order linear differential equations. Adv. Difference...
  • Gordji, M.E., Abbaszadeh, S.: Theory of Approximate Functional Equations in Banach Algebras, Inner Product Spaces and Amenable Groups. Academic...
  • G˘avru¸t˘a, P., Jung, S.-M., Li, Y.: Hyers-Ulam stability for second-order linear differential equations with boundary conditions. Electron....
  • Hyers, D.H.: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. U.S.A. 27, 222–224 (1941)
  • Jung, S.-M.: Hyers–Ulam–Rassias Stability of Functional Equations in Nonlinear Analysis. Springer Optimization and Its Applications, vol....
  • Li, Y., Shen, Y.: Hyers–Ulam stability of nonhomogeneous linear differential equations of second order. Int. J. Math. Math. Sci. (2009). https://doi.org/10.1155/2009/576852
  • Li, Y., Shen, Y.: Hyers–Ulam stability of linear differential equations of second order. Appl. Math. Lett. 23(3), 306–309 (2010)
  • Miura, Takeshi: On the Hyers–Ulam stability of a differentiable map. Sci. Math. Jpn. 55(1), 17–24 (2002)
  • Miura, T., Takahasi, S.E., Choda, H.: On the Hyers–Ulam stability of real continuous function valued differentiable map. Tokyo J. Math. 24(2),...
  • Miura, T., Takahasi, S.E., Hayata, T., Tanahashi, K.: Stability of the Banach space valued Chebyshev differential equation. Appl. Math. Lett....
  • Obłoza, M.: Hyers stability of the linear differential equation. Rocznik Nauk.-Dydakt. Prace Mat 13, 259–270 (1993)
  • Obłoza, M.: Connections between Hyers and Lyapunov stability of the ordinary differential equations. Rocznik Nauk.-Dydakt. Prace Mat 14, 141–146...
  • Rassias, J.M., Rassias, M.J.: Leonhard Paul Euler, his life and his work. Int. J. Appl. Math. Stat. 7(Fe07), 8–17 (2007)
  • Rassias, T.M.: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc. 72(2), 297–300 (1978)
  • Rassias, T.M.: On the stability of functional equations and a problem of Ulam. Acta Appl. Math. 62(1), 23–130 (2000)
  • Shen, Y.: The Ulam stability of first-order linear dynamic equations on time scales. Results Math. 72(4), 1881–1895 (2017)
  • Ulam, S.M.: A Collection of Mathematical Problems: Interscience Tracts in Pure and Applied Mathematics, no. 8. Interscience Publishers, New...