References
- R. P. Agarwal, Y. J. Cho and R. Saadati, On Random Topological Structures, Appl. Anal. Vol. 2011, Article ID 762361, 41 pages doi:10.1155/2011/762361.
- T. Aoki, On the stability of the linear transformation in Banach spaces, 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 and S.K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math. 11 (2003), 687-705.
- T. Bag and S.K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems 151 (2005), 513-547. https://doi.org/10.1016/j.fss.2004.05.004
- Y. J. Cho, M. Eshaghi Gordji and S. Zolfaghari, Solutions and Stability of Generalized Mixed Type QC Functional Equations in Random Normed Spaces, Inequal. Appl. Vol. 2010, Article ID 403101, pp. 16.
- Y. J. Cho, C. Park and R. Saadati, Fuzzy Functional Inequalities, J. Comput. Anal. Appl. 13(2011), 305-320.
- Y. J. Cho and R. Saadati, Lattice Non-Archimedean Random Stability of ACQ Functional Equation, Advan. in Diff. Equat. 2011, 2011:31. https://doi.org/10.1186/1687-1847-2011-31
- L. Cadariu and 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 and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Grazer Math. Ber. 346 (2004), 43-52.
- L. Cadariu and V. Radu, Fixed point methods for the generalized stability of functional equations in a single variable, Fixed Point Theory and Applications 2008, Art. ID 749392 (2008).
- S.C. Cheng and J.M. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc. 86 (1994), 429-436.
- Y. Cho, C. Park and R. Saadati, Functional inequalities in non-Archimedean Banach spaces, Appl. Math. Letters 23 (2010), 1238-1242. https://doi.org/10.1016/j.aml.2010.06.005
- P.W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27 (1984), 76-86. https://doi.org/10.1007/BF02192660
- S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg 62 (1992), 59-64. https://doi.org/10.1007/BF02941618
- S. Czerwik, The stability of the quadratic functional equation. in: Stability of mappings of Hyers-Ulam type, (ed. Th.M. Rassias and J.Tabor), Hadronic Press, Palm Harbor, Florida, 1994, 81-91.
- P. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific Publishing Company, New Jersey, Hong Kong, Singapore and London, 2002.
- J. 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. https://doi.org/10.1090/S0002-9904-1968-11933-0
- S. S. Dragomir, Y. J. Cho and J. K. Kim, Subadditivity of some Functionals associated to Jensen's Inequality with Applications, Taiwan. J. Math. 15(2011), 1815-1828.
- C. Felbin, Finite dimensional fuzzy normed linear spaces, Fuzzy Sets and Systems 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 and Th.M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel, 1998.
-
G. Isac and Th.M. Rassias, Stability of
$\psi$ -additive mappings: Appications to nonlinear analysis, Internat. J. Math. Math. Sci. 19 (1996), 219-228. https://doi.org/10.1155/S0161171296000324 - S. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press lnc., Palm Harbor, Florida, 2001.
- A.K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems 12 (1984), 143-154. https://doi.org/10.1016/0165-0114(84)90034-4
- I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 11 (1975), 326-334.
- S.V. Krishna and K.K.M. Sarma, Separation of fuzzy normed linear spaces, Fuzzy Sets and Systems 63 (1994), 207-217. https://doi.org/10.1016/0165-0114(94)90351-4
- D. Mihet and 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
- M. Mirzavaziri and M.S. Moslehian, A fixed point approach to stability of a quadratic equation, Bull. Braz. Math. Soc. 37 (2006), 361-376. https://doi.org/10.1007/s00574-006-0016-z
- A.K. Mirmostafaee, M. Mirzavaziri and M.S. Moslehian, Fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems 159 (2008), 730-738. https://doi.org/10.1016/j.fss.2007.07.011
- A.K. Mirmostafaee and M.S. Moslehian, Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Sets and Systems 159 (2008), 720-729. https://doi.org/10.1016/j.fss.2007.09.016
- A.K. Mirmostafaee and M.S. Moslehian, Fuzzy approximately cubic mappings, Inform. Sci. 178 (2008), 3791-3798. https://doi.org/10.1016/j.ins.2008.05.032
- M. Mohammadi, Y. J. Cho, C. Park, P. Vetro and R. Saadati, Random Stability of an Additive-quadratic-quartic Functional Equation, J. Inequal. Appl. Vol. 2010, Article ID 754210, pp. 18 pages.
- A. Najati and Y. J. Cho, Generalized Hyers-Ulam Stability of the Pexiderized Cauchy Functional Equation in Non-Archimedean Spaces, Fixed Point Theory Appl. Vol. 2011, Article ID 309026, 11 pages, doi:10.1155/2011/309026.
- A. Najati, J. I. Kang and Y. J. Cho, Local Stability of the Pexiderized Cauchy and Jensen's equations in Fuzzy Spaces, J. Inequal. Appl. 2011, 2011:78 doi:10.1186/1029-242X-2011-78.
- C. Park, Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras, Fixed Point Theory and Applications 2007, Art. ID 50175 (2007).
- C. Park, Generalized Hyers-Ulam-Rassias stability of quadratic functional equations: a fixed point approach, Fixed Point Theory and Applications 2008, Art. ID 493751 (2008).
- 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. Amer. Math. Soc. 72 (1978), 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
- Th.M. Rassias, Problem 16; 2, Report of the 27th International Symp. on Functional Equations, Aequationes Math. 39 (1990), 292-293; 309.
- Th.M. Rassias, On the stability of the quadratic functional equation and its applications, Studia Univ. Babes-Bolyai XLIII (1998), 89-124.
- Th.M. Rassias, The problem of S.M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl. 246 (2000), 352-378. https://doi.org/10.1006/jmaa.2000.6788
- Th.M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), 264-284. https://doi.org/10.1006/jmaa.2000.7046
- Th.M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), 23-130. https://doi.org/10.1023/A:1006499223572
- Th.M. Rassias and P. Semrl, On the behaviour of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc. 114 (1992), 989-993. https://doi.org/10.1090/S0002-9939-1992-1059634-1
- Th.M. Rassias and P. Semrl, On the Hyers-Ulam stability of linear mappings, J. Math. Anal. Appl. 173 (1993), 325-338. https://doi.org/10.1006/jmaa.1993.1070
- Th.M. Rassias and K. Shibata, Variational problem of some quadratic functionals in complex analysis, J. Math. Anal. Appl. 228 (1998), 234-253. https://doi.org/10.1006/jmaa.1998.6129
- R. Saadati and C. Park, Non-Archimedean L-fuzzy normed spaces and stability of functional equations, Computers Math. Appl. 60 (2010), 2488-2496. https://doi.org/10.1016/j.camwa.2010.08.055
- F. Skof, Proprieta locali e approssimazione di operatori, Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129. https://doi.org/10.1007/BF02924890
- S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ. New York, 1960.
- J.Z. Xiao and X.H. Zhu, Fuzzy normed spaces of operators and its completeness, Fuzzy Sets and Systems 133 (2003), 389-399. https://doi.org/10.1016/S0165-0114(02)00274-9