1 |
P. Gavruta, S.-M. Jung, and Y. Li, Hyers-Ulam stability for second-order linear differential equations with boundary conditions, Electron. J. Diff. Equ. 2011 (2011), no. 80, 1-5.
|
2 |
O. Hatori, K. Kobayasi, T. Miura, H. Takagi, and S. E. Takahasi, On the best constant of Hyers-Ulam stability, J. Nonlinear Convex Anal. 5 (2004), no. 3, 387-393.
|
3 |
T. Huuskonen and J. Vaisala, Hyers-Ulam constants of Hilbert spaces, Studia Math. 153 (2002), no. 1, 31-40.
DOI
|
4 |
D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224.
DOI
ScienceOn
|
5 |
D. H. Hyers and S. M. Ulam, On approximate isometries, Bull. Amer. Math. Soc. 51 (1945), 288-292.
DOI
|
6 |
D. H. Hyers and S. M. Ulam, Approximate isometries of the space of continuous functions, Ann. Math. 48 (1947), 285-289.
DOI
|
7 |
D. H. Hyers and S. M. Ulam, On the stability of differential expressions, Math. Mag. 28 (1954), 59-64.
DOI
|
8 |
K.-W. Jun and Y.-H. Lee, A generalization of the Hyers-Ulam-Rassias stability of Jensen's equation, J. Math. Anal. Appl. 238 (1999), no. 1, 305-315.
DOI
ScienceOn
|
9 |
S.-M. Jung, Hyers-Ulam stability of linear differential equations of first order, Appl. Math. Lett. 17 (2004), no. 10, 1135-1140.
DOI
ScienceOn
|
10 |
S.-M. Jung, Hyers-Ulam stability of linear differential equations of first order. III, J. Math. Anal. Appl. 311 (2005), no. 1, 139-146.
DOI
ScienceOn
|
11 |
S.-M. Jung, Hyers-Ulam stability of linear differential equations of first order. II, Appl. Math. Lett. 19 (2006), no. 9, 854-858.
DOI
ScienceOn
|
12 |
T. Miura, H. Oka, S.-E. Takahasi, and N. Niwa, Hyers-Ulam stability of the first order linear differential equation for Banach space-valued holomorphic mappings, J. Math. Inequal. 3 (2007), no. 3, 377-385.
|
13 |
M. Ob loza, Hyers stability of the linear differential equation, Rocznik Nauk.-Dydakt. Prace Mat. 13 (1993), 259-270.
|
14 |
M. Ob loza, Connections between Hyers and Lyapunov stability of the ordinary differential equations, Rocznik Nauk.-Dydakt. Prace Mat. 14 (1997), 141-146.
|
15 |
M. Omladic and P. Semrl, On non linear perturbations of isometries, Math. Ann. 303 (1995), no. 1, 617-628.
DOI
|
16 |
C.-G. Park, On the stability of the linear mapping in Banach modules, J. Math. Anal. Appl. 275 (2002), no. 2, 711-720.
DOI
ScienceOn
|
17 |
D. Popa and I. Rasa, Hyers-Ulam stability of the linear differential operator with non-constant coefficients, Appl. Math. Comput. 219 (2012), no. 4, 1562-1568.
DOI
ScienceOn
|
18 |
V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory 4 (2003), no. 1, 91-96.
|
19 |
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300.
DOI
ScienceOn
|
20 |
J. M. Rassias, On approximation of approximately linear mappings by linear mappings, J. Funct. Anal. 46 (1982), no. 1, 126-130.
DOI
|
21 |
Th. M. Rassias and P. Semrl, On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc. 114 (1992), no. 4, 989-993.
DOI
ScienceOn
|
22 |
Th. M. Rassias and P. Semrl, On the Hyers-Ulam stability of linear mappings, J. Math. Anal. Appl. 173 (1993), no. 2, 325-338.
DOI
ScienceOn
|
23 |
D. G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math. Soc. 57 (1951), 223-237.
DOI
|
24 |
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.
|
25 |
T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64-66.
DOI
|
26 |
J. Baker, J. Lawrence, and F. Zorzitto, The stability of the equation f(x+y) = f(x)f(y), Proc. Amer. Math. Soc. 74 (1979), no. 2, 242-246.
DOI
|
27 |
M. Burger, N. Ozawa, and A. Thom, On Ulam stabiltity, Israel J. Math (2012), 1-21.
|
28 |
K. Cieplinski, Applications of fixed point theorems to the Hyers-Ulam stability of functional equations - a survey, Ann. Func. Anal. 3 (2012), no. 1, 151-164.
DOI
|
29 |
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.
DOI
|
30 |
V. A. Faiziev, Th. M. Rassias, and P. K. Sahoo, The space of ()-additive mappings on semigroups, Trans. Amer. Math. Soc. 354 (2002), no. 11, 4455-4472.
DOI
ScienceOn
|
31 |
G. L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), no. 1-2, 143-190.
DOI
|
32 |
Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), 431-434.
DOI
ScienceOn
|
33 |
P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436.
DOI
ScienceOn
|
34 |
Y.-H. Lee, S.-M. Jung, and M. Th. Rassias, On an n-dimensional mixed type additive and quadratic functional equation, Appl. Math. Comput. 228 (2014), 13-16.
DOI
ScienceOn
|
35 |
S.-M. Jung, A fixed point approach to the stability of differential equations y' = F(x, y), Bull. Malays. Math. Sci. Soc. (2) 33 (2010), no. 1, 47-56.
|
36 |
S.-M. Jung, D. Popa, and M. Th. Rassias, On the stability of the linear functional equation in a single variable on complete metric groups, J. Global Optimi. 59 (2014), no. 1, 165-171.
DOI
ScienceOn
|
37 |
Pl. Kannappan, Functional Equations and Inequalities with Applications, Springer, New York, 2009.
|
38 |
Y. Li, Hyers-Ulam stability of linear differential equations , Thai J. Math. 8 (2010), no. 2, 215-219.
|
39 |
Y. Li and Y. Shen, Hyers-Ulam stability of nonhomogeneous linear differential equations of second order, Internat. J. Math. Math. Sci 2009 (2009), Article ID 576852, 7 pp.
|
40 |
Y. Li and Y. Shen, Hyers-Ulam stability of linear differential equations of second order, Appl. Math. Lett. 23 (2010), no. 3, 306-309.
DOI
ScienceOn
|
41 |
T. Miura, On the Hyers-Ulam stability of a differentiable map, Sci. Math. Jpn. 55 (2002), no. 1, 17-24.
|
42 |
T. Miura, S.-M. Jung, and S.-E. Takahasi, Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations , J. Korean Math. Soc. 41 (2004), no. 6, 995-1005.
DOI
ScienceOn
|
43 |
T. Miura, M. Miyajima, and S.-E. Takahasi, Hyers-Ulam stability of linear differential operator with constant coefficients, Math. Nachr. 258 (2003), 90-96.
DOI
ScienceOn
|
44 |
P. Semrl and J. Vaisala, Nonsurjective nearisometries of Banach spaces, J. Funct. Anal. 198 (2003), no. 1, 268-278.
DOI
ScienceOn
|
45 |
H. Rezaei and S.-M. Jung, A fixed point approach to the stability of linear differential equations, Bull. Malays. Math. Sci. Soc. (2), in press.
|
46 |
H. Rezaei, S.-M. Jung, and Th. M. Rassias, Laplace transform and Hyers-Ulam stability of linear differential equations, J. Math. Anal. Appl. 403 (2013), no. 1, 244-251.
DOI
ScienceOn
|
47 |
P. K. Sahoo and Pl. Kannappan, Intoduction to Functional Equations, Chapman and Hall CRC, Boca Raton, Florida, 2011.
|
48 |
S.-E. Takahasi, T. Miura, and S. Miyajima, On the Hyers-Ulam stability of the Banach space-valued differential equation , Bull. Korean Math. Soc. 39 (2002), no. 2, 309-315.
DOI
ScienceOn
|
49 |
S. M. Ulam, A Collection of the Mathematical Problems, Interscience, New York, 1960.
|