Volume 39 | Number 4 | Year 2016 | Article Id. IJMTT-V39P533 | DOI : https://doi.org/10.14445/22315373/IJMTT-V39P533
In this paper, we study the Hyers-Ulam-Rassias stability of the following affine functional equation on 2- Banach space, Random normed space and Intuitionistic random normed space.
[1] A. White, 2-Banach spaces, Doctorial Diss., St. Louis Univ., 1968. [2] A. White, 2-Banach spaces, Math. Nachr. 42 (1969), 43–60.
[3] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci., 27 (1941), 222–224.
[4] K. H. Park and Y. S. Jung, Stability of a cubic functional equation on Groups, Bull. Korean Math. Soc. 41 (2004), 2, 347-357.
[5] 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.
[6] L. Cadariu, P. Gavruta, L. Gavruta, On the stability of functional equations,J. Nonlinear Sci. Appl. 6 (2013), 60-67.
[7] P. Gavruta, A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings, J. Math. Anal. Appl. 184 (1994), 431–436.
[8] S. G¨ahler, 2-metrische R¨aume und ihre topologische Struktur, Math. Nachr. 26 (1963), 115–148.
[9] S. G¨ahler, Lineare 2-normierte R¨aumen, Math. Nachr. 28 (1964), 1–43.
[10] S. G¨ahler, Uber ¨ 2-Banach-R¨aume, Math. Nachr. 42 (1969), 335–347.
[11] S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ., New York, 1960.
[12] Th. M. Rassias, On the stability of the Linear mapping in Banach spaces, Procc. of the Amer. Math. Soc., 72 (1978), 2, 297-300.
[13] Th.M. Rassias, On the Stability of Functional Equations in Banach spaces, J. Math. Anal. Appl., 251 (2000), 264–284.
[14] W.-G. Park, Approximate additive mapping in 2-Banach spaces and related topics, J. Math. Anal. Appl. 376 (2011), 193–202.
[15] A. N. Sherstnev : On the notion of a random normed space. Dpkl. Akad. Nauk SSSR 149 (1963), pp. 280-283 (in Russian).
[16] B. Schweizer and A. Sklar, Probabilistic Metric Spaces. Elsevier, North Holand (1983).
[17] C. Jung, On generalized complete metric spaces. Bull Am Math Soc. 75 (1969), pp. 113–116.
[18] D. Miheţ and V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces. J Math Anal. Appl. 343(2008), pp. 567–572.
[19] D. Miheţ, The stability of the additive Cauchy functional equation in non-Archimedean fuzzy normed spaces. Fuzzy Set Syst. 161 (2010), pp. 2206–2212.
[20] O. Hadžić and E. Pap, Fixed Point Theory in PM-Spaces. Kluwer Academic, Dordrecht (2001)
[21] R. Saadati, J. Park, On the intuitionistic fuzzy topological spaces, Chaos Soliton Fract. 27(2006), pp. 331–344.
[22] S. Chang, J. Rassias and R. Saadati, The stability of the cubic functional equation in intuitionistic random normed spaces, Appl Math Mech. 31 (2010), pp. 21–26.
[23] S. Chang, Y. Cho and Y. Kang, Nonlinear Operator Theory in Probabilistic Metric Spaces. Nova Science Publishers Inc., NewYork (2001)
[24] S. Kutukcu, A. Tuna and A. Yakut, Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations. Appl Math Mech. 28 (2007) pp.799–809.
[25] G. Deschrijver, and EE. Kerre, On the relationship between some extensions of fuzzy set theory. Fuzzy Set Syst. 23 (2003), pp. 227–235.
[26] K. Atanassov, Intuitionistic fuzzy sets. Fuzzy Set Syst. 20 (1986), pp. 87–96.
Dr Meenakshi, "On the Stability of Affine Functional Equations in Various Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 39, no. 4, pp. 252-258, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V39P533