Fuzzy versions of Hyers-Ulam-Rassias theorem

We introduce three reasonable versions of fuzzy approximately additive functions in fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in a fuzzy sense.

[1]  S. Czerwik,et al.  Functional equations and inequalities in several variables , 2002 .

[2]  M. Moslehian Approximately Vanishing of Topological Cohomology Groups , 2005, math/0501015.

[3]  S. K. Samanta,et al.  Fuzzy bounded linear operators , 2005, Fuzzy Sets Syst..

[4]  P. Gǎvruţa,et al.  A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings , 1994 .

[5]  D. H. Hyers On the Stability of the Linear Functional Equation. , 1941, Proceedings of the National Academy of Sciences of the United States of America.

[6]  George Isac,et al.  Stability of Functional Equations in Several Variables , 1998 .

[7]  A. K. Katsaras,et al.  Fuzzy topological vector spaces II , 1981 .

[8]  M. Moslehian,et al.  On the stability of J*-homomorphisms , 2005, math/0501158.

[9]  Alireza Kamel Mirmostafaee,et al.  Fuzzy stability of the Jensen functional equation , 2008, Fuzzy Sets Syst..

[10]  M. Moslehian,et al.  Approximate Homomorphisms of Ternary Semigroups , 2005, math-ph/0511039.

[11]  Jian-zhong Xiao,et al.  Fuzzy normed space of operators and its completeness , 2003, Fuzzy Sets Syst..

[12]  Ivan Kramosil,et al.  Fuzzy metrics and statistical metric spaces , 1975, Kybernetika.

[13]  S. Krishna,et al.  Separation of fuzzy normed linear spaces , 1994 .

[14]  T. Rassias On the stability of the linear mapping in Banach spaces , 1978 .

[15]  Tosio Aoki,et al.  On the Stability of the linear Transformation in Banach Spaces. , 1950 .

[16]  S. K. Samanta,et al.  FINITE DIMENSIONAL FUZZY NORMED LINEAR SPACES , 2003 .

[17]  M. Moslehian,et al.  A fixed point approach to stability of a quadratic equation , 2005, math/0512007.

[18]  S. Ulam Problems in modern mathematics , 1964 .

[19]  C. Felbin,et al.  Finite dimensional fuzzy normed linear space , 1992 .