Approximate fuzzy double derivations and fuzzy Lie *-double derivations

Abstract

Using the fixed point method, we prove the Hyers-Ulam stability of fuzzy double derivations and fuzzy Lie *-double derivations on fuzzy Banach algebras, fuzzy C*-algebras and fuzzy Lie C*-algebras associated with the following additive functional equation of n-Apollonius type Sigma(n)(i=1) f(z - x(i)) = -1/n Sigma(1 ˂= i ˂ j ˂= n) f(x(i) + x(j)) + nf(z - 1/n(2) Sigma(n)(i=1)x(i)) for a fixed integer n with n ˃= 2.