Research article

Approximation of involution in multi-Banach algebras: Fixed point technique

  • Received: 06 December 2020 Accepted: 24 March 2021 Published: 26 March 2021
  • MSC : 39B52, 39B82, 47H10, 46L05

  • 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

    Related Papers:

  • 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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