The stability of a generalized affine functional equation in fuzzy normed spaces

Abstract

In modelling applied problems only partial informations may be known (or) there may be a degree of uncertainty in the parameters used in the model or some measurements may be imprecise. Due to such features, we are tempted to consider the study of functional equations in the fuzzy settings. For the last 40 years, the fuzzy theory has become a very active area of research and a lot of development has been made in the theory of fuzzy sets [1] to find the fuzzy analogues of the classical set theory. This branch finds a wide range of applications in the field of science and engineering. Katsaras [2] introduced an idea of fuzzy norm on a linear space in 1984. In [3], the authors study the stability problems in fuzzy Banach spaces. In [4], Felbin introduced an alternative definition of a fuzzy norm on a linear topological structure of a fuzzy normed linear spaces. Papers [5, 6, 7] are good survey papers, in which results and history on stability are given. In 1940, Ulam [8] raised a question concerning the stability of group homomorphism as follows: Let G1 be a group and G2 a metric group with the metric