Intuitionistic Fuzzy Stability of a Quadratic Functional Equation

The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers’s theorem was generalized by Aoki 3 for additive mappings. In 1978, Rassias 4 generalized Hyers theorem by obtaining a unique linear mapping near an approximate additive mapping. Assume that E1 and E2 are real-normed spaces with E2 complete, f : E1 → E2 is a mapping such that for each fixed x ∈ E1, the mapping t → f tx is continuous on R, and there exist ε > 0 and p ∈ 0, 1 such that