In this research work, we demonstrate the Hyers-Ulam stability for Cauchy-Jensen functional equation in multi-Banach algebras by the fixed point technique. In fact, we prove that for a function which is approximately Cauchy-Jensen in multi Banach algebra, there is a unique involution near it. Next, we show that under some conditions the involution is continuous, the multi-Banach algebra becomes multi-$ C^* $-algebra and the Banach algebra is self-adjoint.
Citation: Ehsan Movahednia, Choonkil Park, Dong Yun Shin. Approximation of involution in multi-Banach algebras: Fixed point technique[J]. AIMS Mathematics, 2021, 6(6): 5851-5868. doi: 10.3934/math.2021346
In this research work, we demonstrate the Hyers-Ulam stability for Cauchy-Jensen functional equation in multi-Banach algebras by the fixed point technique. In fact, we prove that for a function which is approximately Cauchy-Jensen in multi Banach algebra, there is a unique involution near it. Next, we show that under some conditions the involution is continuous, the multi-Banach algebra becomes multi-$ C^* $-algebra and the Banach algebra is self-adjoint.
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Ehsan Movahednia, Choonkil Park, Dong Yun Shin. Approximation of involution in multi-Banach algebras: Fixed point technique[J]. AIMS Mathematics, 2021, 6(6): 5851-5868. doi: 10.3934/math.2021346
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