References
- L. M. Arriola and W. A. Beyer, Stability of the Cauchy functional equation over p-adic fields, Real Anal. Exchange 31 (2005/06), no. 1, 125–132
- Y. S. Cho and H. M. Kim, Stability of functional inequalities with Cauchy-Jensen additive mappings, Abstr. Appl. Anal. (2007), Art. ID 89180, 13 pp https://doi.org/10.1155/2007/89180
- S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific, River Edge, NJ, 2002
- D. Deses, On the representation of non-Archimedean objects, Topology Appl. 153 (2005), no. 5-6, 774–785 https://doi.org/10.1016/j.topol.2005.01.010
- W. Fechner, Stability of a functional inequality associated with the Jordan-von Neumann functional equation, Aequationes Math. 71 (2006), no. 1-2, 149–161 https://doi.org/10.1007/s00010-005-2775-9
- P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431–436 https://doi.org/10.1006/jmaa.1994.1211
- K. Hensel, Uber eine news 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. 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
- K. Jun and H. Kim, On the Hyers-Ulam-Rassias stability problem for approximately k-additive mappings and functional inequalities, Math. Inequal. Appl. 10 (2007), no. 4, 895–908
- S.-M. Jung, Hyers–Ulam–Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, 2001
- S.-M. Jung, Hyers-Ulam-Rassias stability of Jensen's equation and its application, Proc. Amer. Math. Soc. 126 (1998), no. 11, 3137–3143 https://doi.org/10.1090/S0002-9939-98-04680-2
- A. K. Katsaras and A. Beoyiannis, Tensor products of non-Archimedean weighted spaces of continuous functions, Georgian Math. J. 6 (1999), no. 1, 33–44 https://doi.org/10.1023/A:1022926309318
- A. Khrennikov, Non-Archimedean Analysis: quantum paradoxes, dynamical systems and biological models, Mathematics and its Applications, 427. Kluwer Academic Publishers, Dordrecht, 1997
- Z. Kominek, On a local stability of the Jensen functional equation, Demonstratio Math. 22 (1989), no. 2, 499–507
- L. Li, J. Chung, and D. Kim, Stability of Jensen equations in the space of generalized functions, J. Math. Anal. Appl. 299 (2004), no. 2, 578–586
- A. K. Mirmostafaee, M. Mirzavaziri, and M. S. Moslehian, Fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems 159 (2008), no. 6, 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), no. 6, 720–729 https://doi.org/10.1016/j.fss.2007.09.016
- P. J. Nyikos, On some non-Archimedean spaces of Alexandrof and Urysohn, Topology Appl. 91 (1999), 1–23 https://doi.org/10.1016/S0166-8641(97)00239-3
- J. C. Parnami and H. L. Vasudeva, On Jensen's functional equation, Aequationes Math. 43 (1992), no. 2-3, 211–218 https://doi.org/10.1007/BF01835703
- Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297–300
- J. Ratz, On inequalities associated with the Jordan-von Neumann functional equation, Aequationes Math. 66 (2003), no. 1-2, 191–200 https://doi.org/10.1007/s00010-003-2684-8
- M. Sal Moslehian and T. M. Rassias, Stability of functional equations in non-Archimedean spaces, Appl. Anal. Discrete Math. 1 (2007), no. 2, 325–334
- S. M. Ulam, Problems in Modern Mathematics, Science Editions, John Wiley & Sons, 1964
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