1 |
S. M. Ulam, Problems in Modern Mathematics, Science Editions John Wiley & Sons, Inc., New York, 1964.
|
2 |
A. G. White, Jr., 2-Banach spaces, Math. Nachr. 42 (1969), 43-60.
DOI
|
3 |
T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64-66.
DOI
|
4 |
A. Bahyrycz and M. Piszczek, Hyperstability of the Jensen functional equation, Acta Math. Hungar. 142 (2014), no. 2, 353-365.
DOI
|
5 |
D. G. Bourgin, Hyperstability of the Cauchy equation on restricted domains, Acta Math. Hungar. 141 (2013), no. 1-2, 58-67.
DOI
|
6 |
D. Zhang, On hyperstability of generalised linear functional equations in several variables, Bull. Aust. Math. Soc. 92 (2015), no. 2, 259-267.
DOI
|
7 |
T. 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
|
8 |
D. G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16 (1949), 385-397.
DOI
|
9 |
D. G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math. Soc. 57 (1951), 223-237.
DOI
|
10 |
J. Brzdek, Remarks on hyperstability of the Cauchy functional equation, Aequationes Math. 86 (2013), no. 3, 255-267.
DOI
|
11 |
D. G. Bourgin, A hyperstability result for the Cauchy equation, Bull. Aust. Math. Soc. 89 (2014), no. 1, 33-40.
DOI
|
12 |
D. G. Bourgin, Remarks on stability of some inhomogeneous functional equations, Aequationes Math. 89 (2015), no. 1, 83-96.
DOI
|
13 |
J. Brzdek and K. Cieplinski, Hyperstability and superstability, Abstr. Appl. Anal. 2013 (2013), Art. ID 401756, 13 pp.
|
14 |
J. Brzdek, J. Chudziak, and Z. Pales, A fixed point approach to stability of functional equations, Nonlinear Anal. 74 (2011), no. 17, 6728-6732.
DOI
|
15 |
J. Brzdek and A. Pietrzyk, A note on stability of the general linear equation, Aequationes Math. 75 (2008), no. 3, 267-270.
DOI
|
16 |
Y. J. Cho, P. C. S. Lin, S. S. Kim, and A. Misiak, Theory of 2-inner product spaces, Nova Science Publishers, Inc., Huntington, NY, 2001.
|
17 |
Iz. EL-Fassi, Hyperstability of an n-dimensional Jensen type functional equation, Afr. Mat. 27 (2016), no. 7-8, 1377-1389.
DOI
|
18 |
Iz. EL-Fassi and S. Kabbaj, On the hyperstability of a Cauchy-Jensen type functional equation in Banach spaces, Proyecciones J. Math 34 (2015), no. 4, 359-375.
DOI
|
19 |
S. Elumalai, Y. J. Cho, and S. S. Kim, Best approximation sets in linear 2-normed spaces, Commun. Korean Math. Soc. 12 (1997), no. 3, 619-629.
|
20 |
Iz. EL-Fassi, S. Kabbaj, and A. Charifi, Hyperstability of Cauchy-Jensen functional equations, Indag. Math. (N.S.) 27 (2016), no. 3, 855-867.
DOI
|
21 |
R. W. Freese and Y. J. Cho, Geometry of linear 2-normed spaces, Nova Science Publishers, Inc., Hauppauge, NY, 2001.
|
22 |
S. Gahler, Lineare 2-normierte Raume, Math. Nachr. 28 (1964), 1-43.
DOI
|
23 |
S. Gahler, Uber 2-Banach-Raume, Math. Nachr. 42 (1969), 335-347.
DOI
|
24 |
Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), no. 3, 431-434.
DOI
|
25 |
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
|
26 |
E. Gselmann, Hyperstability of a functional equation, Acta Math. Hungar. 124 (2009), no. 1-2, 179-188.
DOI
|
27 |
D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222-224.
DOI
|
28 |
D. H. Hyers, G. Isac, and T. M. Rassias, Stability of functional equations in several variables, Progress in Nonlinear Differential Equations and their Applications, 34, Birkhauser Boston, Inc., Boston, MA, 1998.
|
29 |
S.-M. Jung, Hyers-Ulam Stability of Functional Equation in Mathematical Analysis, Hadronic Press, Palm Harbor, 2001.
|
30 |
S.-M. Jung and M. Th. Rassias, A linear functional equation of third order associated with the Fibonacci numbers, Abstr. Appl. Anal. 2014 (2014), Art. ID 137468, 7 pp.
|
31 |
G. Maksa and Z. Pales, Hyperstability of a class of linear functional equations, Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 17 (2001), no. 2, 107-112.
|
32 |
S.-M. Jung, M. Th. Rassias, and C. Mortici, On a functional equation of trigonometric type, Appl. Math. Comput. 252 (2015), 294-303.
|
33 |
Pl. Kannappan, Functional Equations and Inequalities with Applications, Springer Monographs in Mathematics, Springer, New York, 2009.
|
34 |
M. Kuczma, An introduction to the theory of functional equations and inequalities, Prace Naukowe Uniwersytetu Slaskiego w Katowicach, 489, Uniwersytet Slaski, Katowice, 1985.
|
35 |
Y.-H. Lee, On the stability of the monomial functional equation, Bull. Korean Math. Soc. 45 (2008), no. 2, 397-403.
DOI
|
36 |
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.
|
37 |
G.V. Milovanovic and M.Th. Rassias (eds.), Analytic Number Theory, Approximation Theory and Special Functions, Springer, New York, 2014.
|
38 |
M. Piszczek, Remark on hyperstability of the general linear equation, Aequationes Math. 88 (2014), no. 1-2, 163-168.
DOI
|
39 |
D. Popa, Hyers-Ulam-Rassias stability of the general linear equation, Nonlinear Funct. Anal. Appl. 7 (2002), no. 4, 581-588.
|
40 |
D. Popa, On the stability of the general linear equation, Results Math. 53 (2009), no. 3-4, 383-389.
DOI
|
41 |
T. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300.
DOI
|
42 |
T. M. Rassias, On a modified Hyers-Ulam sequence, J. Math. Anal. Appl. 158 (1991), no. 1, 106-113.
DOI
|