REFERENCES
[1] M. R. Abdollahpour and A. Najati, Stability of linear differential equations of third order,
Appl. Math. Lett. Volume 24, Issue 11 (2011) 1827–1830.
[2] C. Alsina and R. Ger, On some inequalities and stability results related to the exponential
function, J. Inequal. Appl. 2 (1998) 373–380.
[3] D. R. Anderson, Hyers–Ulam stability of higher-order Cauchy-Euler dynamic equations on
time scales, Dynamic Sys. Appl., 22 (2013), to appear.
[4] D. R. Anderson, B. Gates, and D. Heuer, Hyers-Ulam stability of second-order linear dynamic
equations on time scales, Communications Appl. Anal. 16:3 (2012) 281–292.
[5] Szil´ard Andr´as and Alpar Richard Meszaros, Ulam-Hyers stability of dynamic equations on
time scales via Picard operators Appl. Math. Computation 219 (2013) 4853–4864.
[6] M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications,
Birkh¨auser, Boston, 2001.
[7] N. Brillou¨et-Belluot, J. Brzd¸ek, and K. Ciepli´nski, On some recent developments in Ulam’s
type stability, Abstract Appl. Anal. Volume 2012, Article ID 716936, 41 pages.
[8] P. Gavrut¸a and L. Gavrut¸a, A new method for the generalized Hyers-Ulam-Rassias stability,
Int. J. Nonlinear Anal. Appl. 1 (2010) No.2, 11–18.
[9] P. G˘avrut¸a, S. M. Jung, and Y. J. Li, Hyers-Ulam stability for second-order linear differential
equations with boundary conditions, Electronic J. Diff. Equations Vol. 2011 (2011), No. 80, pp. 1–5.
[10] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941) 222–224.
[11] S.-M. Jung, Hyers–Ulam stability of linear differential equations of first order (I), International
J. Appl. Math. & Stat. Vol. 7, No. Fe07 (2007) 96–100.
[12] S.-M. Jung, Hyers–Ulam stability of linear differential equation of the first order (III), J. Math.
Anal. Appl. 311 (2005) 139–146.
[13] S.-M. Jung, Hyers–Ulam stability of linear differential equations of first order (II), Appl. Math.
Lett. 19 (2006) 854–858.
[14] S.-M. Jung, Hyers–Ulam stability of a system of first order linear differential equations with
constant coefficients, J. Math. Anal. Appl. 320 (2006) 549–561.
[15] S.-M. Jung, Approximate solutions of a linear differential equation of third order, Bull. Malays.
Math. Sci. Soc. (2) 35 (4) (2012) 1063–1073.
[16] S.-M. Jung, B. Kim, and Th. M. Rassias, On the Hyers-Ulam stability of a system of Euler
differential equations of first order, Tamsui Oxford J. Math. Sciences 24(4) (2008) 381–388.
[17] Y. J. Li and Y. Shen, Hyers–Ulam stability of linear differential equations of second order,
Appl. Math. Lett. 23 (2010) 306–309.
[18] Y. J. Li and Y. Shen, Hyers–Ulam stability of nonhomogeneous linear differential equations
of second order, International J. Math. & Mathematical Sciences Vol. 2009 (2009), Article ID 576852, 7 pages.
[19] T. Miura, G. Hirasawa, S. E. Takahasi, and T. Hayata, A characterization of the stability of a
system of the Banach space valued differential equations, Math. Inequalities & Appl. Volume
16, Number 3 (2013), 717–728.
[20] T. Miura, S. Miyajima, and S. E. Takahasi, A characterization of Hyers–Ulam stability of first
order linear differential operators, J. Math. Anal. Appl. Vol. 286, Issue 1 (2003) 136–146.
[21] T. Miura, S. Miyajima, and S. E. Takahasi, Hyers–Ulam stability of linear differential operator
with constant coefficients, Math. Nachr. 258 (2003) 90–96.
[22] T. Miura, H. Oka, H. Takagi, and S. E. Takahasi, A Cauchy-Euler type factorization of operators,
Tokyo J. of Math. Volume 31, Number 2 (2008) 489–493.
[23] C. Mortici, Th. M. Rassias, and S.-M. Jung, The inhomogeneous Euler equation and its HyersUlam
stability, Appl. Math. Letters 40 (2015) 23–28.
[24] M. Obloza, Hyers stability of the linear differential equation, Rocznik Naukowo-Dydaktyczny
Prace Matematyczne 13 (1993), pp. 259–270.
[25] D. Popa and I. Ra¸sa, On the Hyers–Ulam stability of the linear differential equation, J. Math.
Anal. Appl. 381 (2011) 530–537.
[26] D. Popa and I. Ra¸sa, Hyers-Ulam stability of the linear differential operator with nonconstant
coefficients, Appl. Math. Computation 219 (2012) 1562–1568.
[27] Th. M. Rassias, On the stability of linear mapping in Banach spaces, Proc. Amer. Math. Soc.
72 (1978) 297–300.
[28] H. Rezaei, S.-M. Jung, Th. M. Rassias, Laplace transform and Hyers-Ulam stability of linear
differential equations, J. Math. Anal. Appl. 403 (2013) 244–251.
[29] I. A. Rus, Ulam stability of ordinary differential equations, Stud. Univ. Babe¸s-Bolyai Math.
54 (2009) 125–134.
[30] C Tun¸c and E. Bi¸cer, Hyers-Ulam stability of non-homogeneous Euler equations of third and
fourth order, Scientific Research and Essays Vol. 8(5), pp. 220–226, 4 February 2013.
[31] S. M. Ulam, A Collection of the Mathematical Problems, Interscience, New York, 1960.
[32] G. Wang, M. Zhou, and L. Sun, Hyers–Ulam stability of linear differential equations of first
order, Appl. Math. Lett. 21 (2008) 1024–1028.