Acknowledgement
Dong Yun Shin was supported by the University of Seoul in 2019.
References
- T. Aoki: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Japan 2 (1950), 64-66. https://doi.org/10.2969/jmsj/00210064
- T. Bag & S.K. Samanta: Finite dimensional fuzzy normed linear spaces. J. Fuzzy Math. 11 (2003), 687-705.
- T. Bag & S.K. Samanta: Fuzzy bounded linear operators. Fuzzy Sets Syst. 151 (2005), 513-547. https://doi.org/10.1016/j.fss.2004.05.004
- L. Cadariu & V. Radu: Fixed points and the stability of Jensen's functional equation. J. Inequal. Pure Appl. Math. 4, no. 1, Art. ID 4 (2003).
- L. Cadariu & V. Radu: On the stability of the Cauchy functional equation: a fixed point approach. Grazer Math. Ber. 346 (2004), 43-52.
- L. Cadariu & V. Radu: Fixed point methods for the generalized stability of functional equations in a single variable. Fixed Point Theory Appl. 2008, Art. ID 749392 (2008).
- I. Chang & Y. Lee: Additive and quadratic type functional equation and its fuzzy stability, Results Math. 63 (2013), 717-730. https://doi.org/10.1007/s00025-012-0229-y
- S.C. Cheng & J.M. Mordeson: Fuzzy linear operators and fuzzy normed linear spaces. Bull. Calcutta Math. Soc. 86 (1994), 429-436.
- J. Diaz & B. Margolis: A fixed point theorem of the alternative for contractions on a generalized complete metric space. Bull. Am. Math. Soc. 74 (1968), 305-309. https://doi.org/10.1090/S0002-9904-1968-11933-0
- C. Felbin: Finite dimensional fuzzy normed linear spaces. Fuzzy Sets Syst. 48 (1992), 239-248. https://doi.org/10.1016/0165-0114(92)90338-5
- P. Gavruta: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J. Math. Anal. Appl. 184 (1994), 431-436. https://doi.org/10.1006/jmaa.1994.1211
- D.H. Hyers: On the stability of the linear functional equation. Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
- D.H. Hyers, G. Isac & Th.M. Rassias: Stability of Functional Equations in Several Variables. Birkhauser, Basel, 1998.
-
G. Isac & Th.M. Rassias: Stability of
$\psi$ -additive mappings: Applications to nonlinear analysis. Internat. J. Math. Math. Sci. 19 (1996), 219-228. https://doi.org/10.1155/S0161171296000324 - A.K. Katsaras: Fuzzy topological vector spaces II. Fuzzy Sets Syst. 12 (1984), 143-154. https://doi.org/10.1016/0165-0114(84)90034-4
- I. Kramosil & J. Michalek: Fuzzy metric and statistical metric spaces. Kybernetica 11 (1975), 326-334.
- S.V. Krishna & K.K.M. Sarma: Separation of fuzzy normed linear spaces. Fuzzy Sets Syst. 63 (1994), 207-217. https://doi.org/10.1016/0165-0114(94)90351-4
- D. Mihet & V. Radu: On the stability of the additive Cauchy functional equation in random normed spaces. J. Math. Anal. Appl. 343 (2008), 567-572. https://doi.org/10.1016/j.jmaa.2008.01.100
- A.K. Mirmostafaee, M. Mirzavaziri & M.S. Moslehian: Fuzzy stability of the Jensen functional equation. Fuzzy Sets Syst. 159 (2008), 730-738. https://doi.org/10.1016/j.fss.2007.07.011
- A.K. Mirmostafaee & M.S. Moslehian: Fuzzy versions of Hyers-Ulam-Rassias theorem. Fuzzy Sets Syst. 159 (2008), 720-729. https://doi.org/10.1016/j.fss.2007.09.016
- A.K. Mirmostafaee & M.S. Moslehian: Fuzzy approximately cubic mappings. Inform. Sci. 178 (2008), 3791-3798. https://doi.org/10.1016/j.ins.2008.05.032
- V. Radu: The fixed point alternative and the stability of functional equations. Fixed Point Theory 4 (2003), 91-96.
- Th.M. Rassias: On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72 (1978), 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
- S.M. Ulam: A Collection of the Mathematical Problems. Interscience Publ. New York, 1960.
- J.Z. Xiao & X.H. Zhu: Fuzzy normed spaces of operators and its completeness. Fuzzy Sets Syst. 133 (2003), 389-399. https://doi.org/10.1016/S0165-0114(02)00274-9