Author:
Iz-iddine EL-Fassi ,Samir Kabbaj
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:$$f\left(\frac{x+y}{\alpha}+z\right)+f\left(\frac{x-y}{\alpha}+z\right)=\frac{2}{\alpha} f(x)+2 f(z),$$where $\alpha \in \mathbb{N}_{\geq 2}$.
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