On the stability of \(\alpha\)−Cauchy-Jensen type functional equation in Banach algebras
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DOI:
https://doi.org/10.26637/mjm401/019Abstract
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 \(\alpha \in \mathbb{N}_{\geq 2}\).
Keywords:
Cauchy-Jensentypefunctionalequation, fixedpoint, generalized Hyers-Ulam stability, homomorphism in Banach algebraMathematics Subject Classification:
39A10, 47H10, 39B82- Pages: 169-177
- Date Published: 01-01-2016
- Vol. 4 No. 01 (2016): Malaya Journal of Matematik (MJM)
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