- J. Aczel and J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, 1989.
- R.P. Agarwal, B. Xu and W. Zhang, Stability of functional equations in single variable, J. Math. Anal. Appl. 228 (2003) 852–869.
- C. Alsina, On the stability of a functional equation arising in probabilistic normed spaces, General Inequalities. 5 (1987) 263-271.
- D. Amir, Characterizations of Inner Product Spaces, Birkhuser, Basel, 1986.
- T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan. 2 (1950) 64–66.
- L.M. Arriola and W.A. Beyer, Stability of the Cauchy functional equation over p-adic fields, Real Analysis Exchange. 31 (2005/2006) 125-132.
- J.A. Baker, The stability of certain functional equations, Proc. Amer. Math. Soc. 112 (1991) 729–732.
- E. Baktash, Y.J. Cho, M. Jalili, R. Saadati and S.M. Vaezpour, On the stability of cubic mappings and quadratic mappings in random normed spaces, J. Inequal. Appl., Volume 2008, Article ID 902187.
- Y. Benyamini and J. Lindenstrauss, Geometric Nonlinear Functional Analysis, vol. 1, Colloq. Publ. vol. 48, Amer. Math. Soc., Providence, RI, 2000.
- S.S. Chang, Y.J. Cho and S.M. Kang, Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers, Inc., New York, 2001.
- L. C˘adariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Grazer Mathematische Berichte, 346 (2004) 43-52.
- L. C˘adariu and V. Radu, Fixed points and the stability of Jensens functional equation, Journal of Inequalities in Pure and Applied Mathematics, vol. 4, no. 1, article 4, 7 pages, 2003.
- P.W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27 (1984) 76–86.
- P. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific Publishing Company, New Jersey, Hong Kong, Singapore, London, 2002.
- S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg. 62 (1992) 59–64.
- M. Eshaghi Gordji and H. Khodaei, Solution and stability of generalized mixed type cubic, quadratic and additive functional equation in quasi–Banach spaces, Nonlinear Analysis.-TMA. 71 (2009) 5629–5643.
- M. Eshaghi Gordji and H. Khodaei, On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations, Abstract and Applied Analysis Volume 2009, Article ID 923476, 11 pages.
- M. Eshaghi Gordji, H. Khodaei and C. Park, A fixed point approach to the Cauchy-Rassias stability of general Jensen type quadratic-quadratic mappings, (To appear).
- V.A. Faizev, Th.M. Rassias and P.K. Sahoo, The space of (ψ, γ)–additive mappings on semigroups, Trans. Amer. Math. Soc. 354 (11) (2002) 4455–4472.
- Z. Gajda, On stability of additive mappings, Int. J. Math. Math. Sci. 14 (1991) 431–434.
- P. Gˇavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994) 431-436.
- P. Gˇavruta, An answer to a question of Th.M. Rassias and J. Tabor on mixed stability of mappings, Bul. Stiint. Univ. Politeh. Timis. Ser. Mat. Fiz. 42 (56) (1997) 1–6.
- P. Gˇavruta, On the Hyers–Ulam–Rassias stability of mappings, Recent Progress in Inequalities. 430 (1998) 465–469.
- P. Gˇavruta, An answer to a question of John M. Rassias concerning the stability of Cauchy equation, in: Advances in Equations and Inequalities, Hadronic Math. Ser. (1999) 67–71.
- P. Gˇavruta, On a problem of G. Isac and Th.M. Rassias concerning the stability of mappings, J. Math. Anal. Appl. 261 (2001) 543–553.
- P. Gˇavruta, On the Hyers–Ulam–Rassias stability of the quadratic mappings, Nonlinear Funct. Anal. Appl. 9 (2004) 415–428.
- P. Gˇavruta, M. Hossu, D. Popescu and C. Cˇaprˇau, On the stability of mappings and an answer to a problem of Th.M. Rassias, Ann. Math. Blaise Pascal. 2 (1995) 55–60.
- A. Grabiec, The generalized Hyers–Ulam stability of a class of functional equations, Publ. Math. Debrecen. 48 (1996) 217–235.
- O. Hadˇzi´c and E. Pap, Fixed Point Theory in PM Spaces, Kluwer Academic Publishers, Dordrecht. 2001.
- O. Hadˇzi´c, E. Pap and M. Budincevi´c, Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces, Kybernetica, 38 (3) (2002) 363–381.
- K. Hensel, Uber eine neue Begrundung der Theorie der algebraischen Zahlen, Jahresber. Deutsch. Math. Verein. 6 (1897) 83-88.
- D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. 27 (1941) 222–224.
- D.H. Hyers, G. Isac and Th.M. Rassias, Stability of Functional Equations in Several Variables, Birkhuser, Basel, 1998.
- D.H. Hyers and Th.M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992) 125–153.
- D.H. Hyers, G. Isac and Th.M. Rassias, Topics in Nonlinear Analysis and Applications, World Scientific Publishing Company, 1997.
- G. Isac and Th.M. Rassias, Stability of ψ–additive mappings: Applications to nonlinear analysis, Internat. J. Math. Math. Sci. 19 (1996) 219–228.
- P. Jordan and J. Neumann, On inner products in linear metric spaces, Ann. Math. 36 (1935) 719–723.
- S.-M. Jung, Hyers–Ulam–Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press Inc., Palm Harbor, Florida, 2001.
- S.-M. Jung and T.-S. Kim, A fixed point approach to stability of cubic functional equation, Bol. Soc. Mat. Mexicana 12 (2006) 51–57.
- Y.S. Jung and L.S. Chang, The stability of a cubic type functional equation with The fixed point alternative, J. Math. Anal. Appl. 306 (2005) 752–760.
- Pl. Kannappan, Quadratic functional equation and inner product spaces, Results Math. 27 (1995) 368–372.
- A. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer Academic Publishers, Dordrecht, 1997.
- B. Margolis and J.B. Diaz, A fixed point theorem of the alternative for contractions on the generalized complete metric space, Bull. Amer. Math. Soc. 126 74 (1968) 305–309.
- D. Mihet¸, Fuzzy stability of additive mappings in non-Archimedean fuzzy normed spaces, Fuzzy Sets and Systems (communicated).
- D. Mihet¸, The probabilistic stability for a functional equation in a single variable, Acta Math. Hungar. 123 (2009) 249–256.
- D. Mihet¸, The fixed point method for fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems. 160 (2009) 1663–1667.
- 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.
- D. Mihet¸, R. Saadati and S.M. Vaezpour, The stability of the quartic functional equation in random normed spaces, Acta Appl. Math., DOI: 10.1007/s10440-009-9476-7.
- D. Mihet¸, R. Saadati and S.M. Vaezpour, The stability of an additive functional equation in Menger probabilistic ϕ-normed spaces, Math. Slovak, in press.
- A.K. Mirmostafaee, M. Mirzavaziri and M.S. Moslehian, Fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems. 159 (2008) 730–738.
- A.K. Mirmostafaee and M.S. Moslehian, Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Sets and Systems. 159 (2008) 720–729.
- A.K. Mirmostafaee and M.S. Moslehian, Fuzzy approximately cubic mappings, Inform. Sci. 178 (2008) 3791–3798.
- M. Mirzavaziri and M.S. Moslehian, A fixed point approach to stability of a quadratic equation, Bull. Braz. Math. Soc. 37 (2006) 361–376.
- M.S. Moslehian and T.M. Rassias, Stability of functional equations in non-Archimedean space, Applicable Analysis and Discrete Mathematics. 1 (2007) 325-334.
- 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.
- Th.M. Rassias, New characterization of inner product spaces, Bull. Sci. Math. 108 (1984) 95–99.
- Th.M. Rassias, Functional Equations, Inequalities and Applications, Kluwer Academic Publishers Co., Dordrecht, Boston, London, 2003.
- Th.M. Rassias, Problem 16; 2, Report of the 27th International Symp. on Functional Equations, Aequationes Math. 39 (1990) 292–293.
- 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.
- Th.M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000) 264–284.
- Th.M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000) 23–130.
- Th.M. Rassias and P. Semrl, ˇ On the behaviour of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc. 114 (1992) 989–993.
- Th.M. Rassias and P. Semrl, ˇ On the Hyers-Ulam stability of linear mappings, J. Math. Anal. Appl. 173 (1993) 325–338.
- Th.M. Rassias and K. Shibata, Variational problem of some quadratic functionals in complex analysis, J. Math. Anal. Appl. 228 (1998) 234–253.
- A. M. Robert, A Course in p-adic Analysis, Springer-Verlag, New York, 2000.
- S. Rolewicz, Metric Linear Spaces, PWN-Polish Sci. Publ./Reidel, Warszawa/Dordrecht, 1984.
- I.A. Rus, Principles and Applications of Fixed Point Theory, Ed. Dacia, Cluj-Napoca, 1979 (in Romanian).
- R. Saadati, S.M. Vaezpour and Y.J. Cho, A note on the ”On the stability of cubic mappings and quadratic mappings in random normed spaces”, J. Inequal. Appl., Volume 2009, Article ID 214530, 6 pages.
- B. Schweizer and A. Sklar, Probabilistic Metric Spaces, Elsevier, North Holand, New York, 1983.
- A.N. Serstnev, ˇ On the notion of a random normed space, Dokl. Akad. Nauk SSSR 149 (1963) 280-283 (in Russian).
- J. Tabor, stability of the Cauchy functional equation in quasi-Banach spaces, Ann. Polon. Math. 83 (2004) 243–255.
- S.M. Ulam, Problems in Modern Mathematics, Chapter VI, science Editions., Wiley, New York, 1964.
- A.C.M. Van rooij, Non-Archimedean functional analysis, in: Monographs and Textbooks in Pure and Applied Math, vol. 51, Marcel Dekker, New York, 1978.
- V.S. Vladimirov, I.V. Volovich and E.I. Zelenov, p–adic Analysis and Mathematical Physics, World Scientific, 1994.
|