Fixed Points and Fuzzy Stability of Functional Equations Related to Inner Product

In [40], Th.M. Rassias introduced the following equality for a fixed integer . Let be real vector spaces. It is shown that if a mapping satisfies (0.1) for all with , then the mapping is realized as the sum of an additive mapping and a quadratic mapping. From the above equality we can define the functional equation which is called a quadratic functional equation. Every solution of the quadratic functional equation is said to be a quadratic mapping. Using fixed point theorem we prove the Hyers-Ulam stability of the functional equation (0.1) in fuzzy Banach spaces.