Stability of General Cubic Mapping in Fuzzy Normed Spaces

[1] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan., 2 (1950), 64-66.10.2969/jmsj/00210064Search in Google Scholar

[2] C. Baak and M. S. Moslehian, On the stability of orthogonally cubic functional equations, Kyungpook. Math. J., 47 (2007), 69-76.Search in Google Scholar

[3] T. Bag and S. K. Samanta, Finite dimentional fuzzy normed linear spaces, J. Fuzzy Math., 11 (2003), 687-705.Search in Google Scholar

[4] T. Bag and S. K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151 (2005), 513-547.10.1016/j.fss.2004.05.004Search in Google Scholar

[5] V. Balopoulos, A. G. Hatzimichailidis and B. K. Papadopoulos, Distance and Similarity measures for fuzzy operators, Inform. Sci., 177 (2007), 2336-2348.10.1016/j.ins.2007.01.005Search in Google Scholar

[6] R. Biswas, Fuzzy inner product spaces and fuzzy normed functions, Inform. Sci., 53 (1991), 185-190.10.1016/0020-0255(91)90063-ZSearch in Google Scholar

[7] S.C. Cheng and J. N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calutta Math. Soc., 86 (1994), 429-436.Search in Google Scholar

[8] W. Congxin and J. Fang, Fuzzy generalization of klomogoroffs theorem, J. Harbin Inst. Technol., 1 (1984), 1-7.Search in Google Scholar

[9] S. Czerwik, Functional equations and Inequalities in Several Variables, World scientific, River Edge, NJ, 2002.10.1142/4875Search in Google Scholar

[10] C. Felbin, Finit dimensional fuzzy normed linear spaces, Fuzzy Sets and Systems, 48 (1992), 239-248.10.1016/0165-0114(92)90338-5Search in Google Scholar

[11] A. Ghaffari and A. Alinejad, Stabilities of cubic Mappings in Fuzzy Normed Spaces, Advances in Difference Equations, vol. 2010 (2010), 15 pages.10.1155/2010/150873Search in Google Scholar

[12] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA, 27 (1941), 222-224.10.1073/pnas.27.4.222Search in Google Scholar

[13] D. H. Hyers, G. Isac and Th. M. Rassias, Stability of Functional Equationsin Several Variables, Birkhuser, Basel, 1998.10.1007/978-1-4612-1790-9Search in Google Scholar

[14] K. W. Jun and H. M. Kim, The generalized Hyers-Ulam-Rassias stability of a cubic functional equation, J. Math. Anal. Appl., 274 (2002), 867-878.10.1016/S0022-247X(02)00415-8Search in Google Scholar

[15] K. W. Jun, H. M. Kim and I.-S. Chang, On the Hyers-Ulam stability of an Euler-Lagrang type cubic functional equation, J. Comput. Anal. Appl., 7 (2005), 21-33.Search in Google Scholar

[16] S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, 2001.Search in Google Scholar

[17] S.-M. Jung and T.-S. Kim, A fixed point approach to the stability of cubic functional equation, Bol. Soc. Mat. Mexicana, 12 (1) (2006), 51-57.Search in Google Scholar

[18] A. K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984), 143-15410.1016/0165-0114(84)90034-4Search in Google Scholar

[19] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11 (1975), 326-334.Search in Google Scholar

[20] S. V. Krishna and K. K. M. Sarma, Seperation of fuzzy normed linear spaces, Fuzzy Sets and Systems, 63 (1994), 207-217.10.1016/0165-0114(94)90351-4Search in Google Scholar

[21] A. Najati, The generalized Hyers-Ulam-Rassias stability of a cubic functional equation, Turkish J. Math., 31 (2007), 395-408.Search in Google Scholar

[22] Th. M. Rassias, On the stability of linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300. 10.1090/S0002-9939-1978-0507327-1Search in Google Scholar

[23] Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math., 62 (2000), 23-130.10.1023/A:1006499223572Search in Google Scholar

[24] Th. M. Rassias, Functional equations, In equalities and Applications, Kluwer Academic Publishers, Dordecht, Boston, London, 2003.10.1007/978-94-017-0225-6Search in Google Scholar

[25] J. M. Rassias, Solution of Ulam stability problem for cubic mappings, Glas. Mat. Ser. III, 36 (2001), 63-72.Search in Google Scholar

[26] P. K. Sahoo, A generalized cubic functioal equation, Acta. Math. Sin. (Engl. ser.), 21 (2005), 1159-1166.10.1007/s10114-005-0551-3Search in Google Scholar

[27] B. Shieh, Infinite fuzzy relation equations with continuous t-norms, Inform. Sci., 178 (2008), 1961-1967.10.1016/j.ins.2007.12.006Search in Google Scholar

[28] S. M. Ulam, Some equations in analysis, Stability, Problems in Modern Mathematics, Science eds., Wiley, New York, 1964.Search in Google Scholar

[29] J. Z. Xiao and X. H. Zhu, Fuzzy normed space of operators and its completeness, Fuzzy Sets and Systems 133 (2003), 389-399.10.1016/S0165-0114(02)00274-9Search in Google Scholar

[30] T. Z. Xu, Generalized Ulam-Hyers stability of a general mixed AQCQ functional equation in multi-Banach spaces: A fixed point approach, European Journal of pure and Applied Mathematics, vol. 3 (2010), 1032-1047.Search in Google Scholar

[31] T. Z. Xu, J. M. Rassias and W. X. Xu, Stability of a general mixed additive-cubic functional equationin non-Archimedean fuzzy normed spaces, Journal of Mathematical Physics, vol. 51 (2010), 19 pages.10.1063/1.3482073Search in Google Scholar

[32] T. Z. Xu, J. M. Rassias and W. X. Xu, A fixed point approach to the stability of a general mixed additive-cubic functional equation in quasifuzzy normed spaces, International Journal of Physical Sciences, 6 (2011), 313-324.Search in Google Scholar

[33] T. Z. Xu, J. M. Rassias and W. X. Xu, Intuitionistic fuzzy stability of ageneral mixed additive-cubic equation, Journal of Mathematical Physics, vol. 51 (2010), 21 pages.10.1063/1.3431968Search in Google Scholar

[34] T. Z. Xu, J. M. Rassias and W. X. Xu, A fixed point approach to the stability of a general mixed AQCQ-functional equation in non-Archimedean normed spaces, Discrete Dynamics in Nature and Society, vol. 2010 (2010), 24 pages. 10.1155/2010/812545Search in Google Scholar

[35] T. Z. Xu, J. M. Rassias and W. X. Xu, On the stability of a general mixedadditive-cubic functional equation in random normed spaces, Journal of Inequalities and Applications, Vol. 2010, Article ID 328473, 16 pages, 2010. Search in Google Scholar