A fixed point approach to the stability of differential equations y′ = F(x,y)

Bulletin of the Malaysian Mathematical Sciences Society

Volumn 33, Issue 1, 2010, Pages 47-56

  Jung, Soon Mo ^a  

^a Hong Ik University   (South Korea)

Author keywords

Differential equation; Fixed point method; Hyers ulam stability; Hyers ulam rassias stability

Indexed keywords

EID: 74849112184     PISSN: 01266705     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. C. Alsina and R. Ger, On some inequalities and stability results related to the exponential function, J. Inequal. Appl. 2 (1998), no. 4, 373-380.
2. L. Cǎdariu and V. Radu, Fixed points and the stability of Jensen's functional equation, JIPAM. J. Inequal. Pure Appl. Math. 4 (2003), no. 1, Article 4, 7 pp. (electronic)
3. L. Cǎdariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, in Iteration Theory (ECIT'02), 43-52, Karl-Franzens-Univ. Graz, Graz, Austria.
4. J. B. Diaz and B. Margolis, A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968), 305-309.
5. D. H. Hyers, G. Isac and T. M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser Boston, Boston, MA, 1998.
6. S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, FL, 2001.
7. S.-M. Jung, Hyers-Ulam stability of linear differential equations of first order, Appl. Math. Lett. 17 (2004), no. 10, 1135-1140.
8. S.-M. Jung, Hyers-Ulam stability of linear differential equations of first order. II, Appl. Math. Lett. 19 (2006), no. 9, 854-858.
9. S.-M. Jung, Hyers-Ulam stability of a system of first order linear differential equations with constant coefficients, J. Math. Anal. Appl. 320 (2006), no. 2, 549-561.
10. S.-M. Jung, A fixed point approach to the stability of isometries, J. Math. Anal. Appl. 329 (2007), no. 2, 879-890.
11. T. Miura, S.-M. Jung and S.-E. Takahasi, Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations y′ = λy, J. Korean Math. Soc. 41 (2004), no. 6, 995-1005.
12. T. Miura, S. Miyajima and S.-E. Takahasi, A characterization of Hyers-Ulam stability of first order linear differential operators, J. Math. Anal. Appl. 286 (2003), no. 1, 136-146.
13. T. Miura, S. Miyajima and S.-E. Takahasi, Hyers-Ulam stability of linear differential operator with constant coefficients, Math. Nachr. 258 (2003), 90-96.
14. M. Obloza, Hyers stability of the linear differential equation, Rocznik Nauk.-Dydakt. Prace Mat. No. 13 (1993), 259-270.
15. M. Obloza, Connections between Hyers and Lyapunov stability of the ordinary differential equations, Rocznik Nauk.-Dydakt. Prace Mat. No. 14 (1997), 141-146.
16. V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory 4 (2003), no. 1, 91-96.
17. S.-E. Takahasi, T. Miura and S. Miyajima, On the Hyers-Ulam stability of the Banach space-valued differential equation y′ = λy, Bull. Korean Math. Soc. 39 (2002), no. 2, 309-315.