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

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,...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 6; pp. 5851 - 5868
Main Authors Movahednia, Ehsan, Park, Choonkil, Shin, Dong Yun
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
c∗-algebra
fixed point technique
functional equation
hyers-ulam stability
multi-banach algebra
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021346