A general uniqueness theorem concerning the stability of monomial functional equations in fuzzy spaces

Abstract

In this paper, we prove a general uniqueness theorem that can easily be applied to the (generalized) Hyers-Ulam stability of a large class of functional equations, which includes monomial functional equations (e.g. the Cauchy additive functional equation, the quadratic functional equation, and the cubic functional equation, etc.). This uniqueness theorem can save us much trouble in proving the uniqueness of relevant solutions repeatedly appearing in the stability problems for functional equations in fuzzy spaces.