참고문헌
- J. Aczel and J. Dhombres, Functional Equations in Several Variables, Cambridge Univ. Press, Cambridge, 1989.
- 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
- D.G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math. Soc. 57(1951), 223-237. https://doi.org/10.1090/S0002-9904-1951-09511-7
- S.S. Chang, Y.J. Cho and S.M. Kang, Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers Inc. New York, 2001.
- P.W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27(1984), 76-86. https://doi.org/10.1007/BF02192660
- J.K. Chung and P.K. Sahoo, On the general solution of a quartic functional equation, Bull. Korean Math. Soc. 40(2003), 565-576. https://doi.org/10.4134/BKMS.2003.40.4.565
- S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Semin. Univ. Hambg. 62(1992), 59-64. https://doi.org/10.1007/BF02941618
- Z. Gajda, On stability of additive mappings, Int. J. Math. Math. Sci. 14(1991), 431-434. https://doi.org/10.1155/S016117129100056X
- 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
- A. Grabiec, The generalized Hyers-Ulam stability of a class of functional equations, Publ. Math. Debrecen 48(1996), 217-235.
- O. Hadzic and E. Pap, Fixed Point Theory in PM Spaces, Kluwer Academic Publishers, Dordrecht, 2001.
- O. Hadzic, E. Pap and M. Budincevic, Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces, Kybernetika 38(2002), 363-381.
- D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 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, Birkhaer, Basel, 1998.
-
G. Isac and Th.M. Rassias, On the Hyers-Ulam stability of
${\psi}-additive$ mappings, J. Approx. Theory 72(1993), 131-137. https://doi.org/10.1006/jath.1993.1010 - Pl. Kannappan, Quadratic functional equation and inner product spaces, Results Math. 27(1995), 368-372. https://doi.org/10.1007/BF03322841
- D. Mihet, The probabilistic stability for a functional equation in a single variable, Acta Math. Hungar. 123(2009), 249-256. https://doi.org/10.1007/s10474-008-8101-y
- D. Mihet, The fixed point method for fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems 160(2009), 1663-1667. https://doi.org/10.1016/j.fss.2008.06.014
- 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. 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. Mirmostafee 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
- 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, 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, 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
- B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland, New York, 1983.
- A.N. Sherstnev, On the notion of a random normed space, Dokl. Akad. Nauk SSSR 149(1963), 280-283 (in Russian).
- F. Skof, Propriet locali e approssimazione di operatori, Rend. Sem. Mat. Fis. Milano 53(1983), 113-129. https://doi.org/10.1007/BF02924890
- S.M. Ulam, Problems in Modern Mathematics, Chapter VI, Science ed., Wiley, New York, 1940.