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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AIMS Press
2021-04-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/doi/10.3934/math.2021346?viewType=HTML |
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doaj-9c673f9b450f4ee6904791ea8fed47ae2021-04-07T01:49:05ZengAIMS PressAIMS Mathematics2473-69882021-04-01665851586810.3934/math.2021346Approximation of involution in multi-Banach algebras: Fixed point techniqueEhsan Movahednia0Choonkil Park1Dong Yun Shin 21. Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Behbahan, Iran2. Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea3. Department of Mathematics, University of Seoul, Seoul 02504, KoreaIn 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.http://www.aimspress.com/article/doi/10.3934/math.2021346?viewType=HTMLmulti-banach algebrahyers-ulam stabilityfunctional equationfixed point techniquec∗-algebra |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ehsan Movahednia Choonkil Park Dong Yun Shin |
| spellingShingle |
Ehsan Movahednia Choonkil Park Dong Yun Shin Approximation of involution in multi-Banach algebras: Fixed point technique AIMS Mathematics multi-banach algebra hyers-ulam stability functional equation fixed point technique c∗-algebra |
| author_facet |
Ehsan Movahednia Choonkil Park Dong Yun Shin |
| author_sort |
Ehsan Movahednia |
| title |
Approximation of involution in multi-Banach algebras: Fixed point technique |
| title_short |
Approximation of involution in multi-Banach algebras: Fixed point technique |
| title_full |
Approximation of involution in multi-Banach algebras: Fixed point technique |
| title_fullStr |
Approximation of involution in multi-Banach algebras: Fixed point technique |
| title_full_unstemmed |
Approximation of involution in multi-Banach algebras: Fixed point technique |
| title_sort |
approximation of involution in multi-banach algebras: fixed point technique |
| publisher |
AIMS Press |
| series |
AIMS Mathematics |
| issn |
2473-6988 |
| publishDate |
2021-04-01 |
| description |
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. |
| topic |
multi-banach algebra hyers-ulam stability functional equation fixed point technique c∗-algebra |
| url |
http://www.aimspress.com/article/doi/10.3934/math.2021346?viewType=HTML |
| work_keys_str_mv |
AT ehsanmovahednia approximationofinvolutioninmultibanachalgebrasfixedpointtechnique AT choonkilpark approximationofinvolutioninmultibanachalgebrasfixedpointtechnique AT dongyunshin approximationofinvolutioninmultibanachalgebrasfixedpointtechnique |
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1721537024823918592 |