참고문헌
- 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 and S.K. Samanta, A comparative study of fuzzy norms on a linear space, Fuzzy Sets and Sys., 159 (2008), 670-684. https://doi.org/10.1016/j.fss.2007.09.011
- 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 (2008), Art. ID 749392.
- L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Iteration theory (ECIT '02), 43-52, Grazer Math. Ber., 346, Karl-Franzens-Univ. Graz, Graz, 2004.
- J.K. Chung and P.K. Sahoo, On the general solution of a quartic functional equation, Bulletin of the Korean Mathematical Society, 40 (2003), no. 4, 565-576. https://doi.org/10.4134/bkms.2003.40.4.565
- D.H. Hyers, On the stability of the linear functional equation, Proceedings of the National Academy of Sciences of the United States of America, 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
-
G. Isac and 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 - I.H. Jebril and T.K. Samanta, Fuzzy anti-normed linear space, J. Math. Tech., (2010), 66-77.
- Y.-S. Lee and S.-Y. Chung, Stability of quartic functional equations in the spaces of generalized functions, Adv. Diff. Equa., 2009 (2009), Article ID 838347, 16 pages doi:10.1155/2009/838347.
-
M.A. Khamsi, Quasicontraction Mapping in modular space without
${\Delta}_2$ -condition, Fixed Point Theory and Applications, (2008), Artical ID 916187, 6 pages. - H.-K. Kim and H.-Y. Shin, Refined stability of additive and quadratic functional equations in modular spaces, J. Inequal. Appl., 2017 (2017), DOI 10.1186/s13660-017-1422-z.
- B. Margolis and J.B. Diaz, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 126 (1968), 305-309. https://doi.org/10.1090/S0002-9904-1968-11933-0
- 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
- 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
- H. Nakano, Modulared Semi-Ordered Linear Spaces, Maruzen, Tokyo, 1950.
- C. Park, Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras, Fixed Point Theory Appl., 2007 (2007), Art. ID 50175.
- V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory, 4 (2003), 91-96.
- J.M. Rassias, Solution of the Ulam stability problem for quartic mappings, Glasnik Matematicki Series III, 34 (1999), 243-252.
- 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
- I.A. Rus, Principles and Applications of Fixed Point Theory, Ed. Dacia, Cluj-Napoca, 1979 (in Romanian).
- P.K. Sahoo, A generalized cubic functional equation, Acta Math. Sinica, 21 (2005), 1159-1166. https://doi.org/10.1007/s10114-005-0551-3
- S.M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1960.
- T.Z. Xu, J.M. Rassias, and W.X. Xu, A generalized mixed quadratic-quartic functional equation, Bull. Malaysian Math. Scien. Soc., 35 (2012), 633-649.
- K. Wongkum, P. Kumam, Y.J. Cho, and P. Chaipumya, On the generalized Ulam-Hyers-Rassias stability for quartic functional equation in modular spaces, J. Nonlinear Sci. Appl., 10 (2017), 1-10. https://doi.org/10.22436/jnsa.010.01.01