The stability of Jordan k-*-derivations on Γ∗-Banach algebras by fixed point method

Abstract

Using fixed point methods, we prove the stability and the superstability of Jordan k-∗-derivations on Γ∗-Banach algebras for the following Jensen-type functional equation μf((x+y)/2)+μf((x-y)/2)=f(μx) where μ is a complex number such that |μ| = 1. We also investigate the stability and the superstability of Jordan k-∗-derivations with the functional equation f(2μx+μy)+f(μx+2μy)=μ[f(3x)+f(3y)] on Γ∗-Banach algebras.