On the Stability  of   $\alpha-$Cauchy-Jensen type functional equation in Banach Algebras

Iz-iddine EL-Fassia,* and Samir Kabbajb

On the Stability of $\alpha-$Cauchy-Jensen type functional equation in Banach Algebras

Authors :

Iz-iddine EL-Fassi^a,* and Samir Kabbaj^b

Author Address :

^a,bDepartment of Mathematics, Faculty of Sciences, University of Ibn Tofail, Kenitra, Morocco.

*Corresponding author.

Abstract :

Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras for the following $\alpha-$Cauchy-Jensen functional equation:
\begin{equation*}
f(\frac{x+y}{\alpha}+z)+f(\frac{x-y}{\alpha}+z)=\frac{2}{\alpha}f(x)+2f(z),
\end{equation*}
where $\alpha\in \mathbb{N}_{\geq 2}.

Keywords :

Cauchy-Jensen type functional equation, fixed point, homomorphism in Banach algebra, generalized Hyers-Ulam stability.

DOI :

Article Info :

Received : October 10, 2015; Accepted : January 23, 2016.