Bihomomorphisms and biderivations in Lie Banach algebras
In this paper, we solve the following bi-additive $s$-functional inequality<br /> $\begin{array}{*{20}{c}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\left\| {f(x - y,y + z) + f\left( {y + z,z - x} \right) + f\left( {z + x,x - z} \right) - f\left( {x - y,x + y} \right)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020145/fulltext.html |
| _version_ | 1818096732470247424 |
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| author | Tae Hun Kim Ha Nuel Ju Hong Nyeong Kim Seong Yoon Jo Choonkil Park |
| author_facet | Tae Hun Kim Ha Nuel Ju Hong Nyeong Kim Seong Yoon Jo Choonkil Park |
| author_sort | Tae Hun Kim |
| collection | DOAJ |
| description | In this paper, we solve the following bi-additive $s$-functional inequality<br />
$\begin{array}{*{20}{c}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\left\| {f(x - y,y + z) + f\left( {y + z,z - x} \right) + f\left( {z + x,x - z} \right) - f\left( {x - y,x + y} \right)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left( {0.1} \right)} \right.}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{ \le \left\| {s\left( {f\left( {y - z,z + x} \right) + f\left( {z + x,x - y} \right) + f\left( {x + y,y - x} \right) - f\left( {y - z,y + z} \right)} \right)} \right\|,}\end{array}$<br />
where $s$ is a fixed nonzero complex number satisfying $|s|<1$. Furthermore, we prove the Hyers-Ulam stability of bihomomorphisms and biderivations in Lie Banach algebras associated with the bi-additive $s$-functional inequality (0.1). |
| first_indexed | 2024-12-10T23:09:18Z |
| format | Article |
| id | doaj.art-767f60c5460249099978b712517f316b |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-10T23:09:18Z |
| publishDate | 2020-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-767f60c5460249099978b712517f316b2022-12-22T01:29:59ZengAIMS PressAIMS Mathematics2473-69882020-02-01532196221010.3934/math.2020145Bihomomorphisms and biderivations in Lie Banach algebrasTae Hun Kim0Ha Nuel Ju1Hong Nyeong Kim2Seong Yoon Jo3Choonkil Park41 Mathematics Branch, Seoul Science High School, Seoul 03066, Korea1 Mathematics Branch, Seoul Science High School, Seoul 03066, Korea1 Mathematics Branch, Seoul Science High School, Seoul 03066, Korea1 Mathematics Branch, Seoul Science High School, Seoul 03066, Korea2 Research Institute for Natural Sciences, Hanyang University, Seoul 04763, KoreaIn this paper, we solve the following bi-additive $s$-functional inequality<br /> $\begin{array}{*{20}{c}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\left\| {f(x - y,y + z) + f\left( {y + z,z - x} \right) + f\left( {z + x,x - z} \right) - f\left( {x - y,x + y} \right)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left( {0.1} \right)} \right.}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{ \le \left\| {s\left( {f\left( {y - z,z + x} \right) + f\left( {z + x,x - y} \right) + f\left( {x + y,y - x} \right) - f\left( {y - z,y + z} \right)} \right)} \right\|,}\end{array}$<br /> where $s$ is a fixed nonzero complex number satisfying $|s|<1$. Furthermore, we prove the Hyers-Ulam stability of bihomomorphisms and biderivations in Lie Banach algebras associated with the bi-additive $s$-functional inequality (0.1).https://www.aimspress.com/article/10.3934/math.2020145/fulltext.htmlhyers-ulam stabilitybi-additive s-functional inequalitylie banach algebrabihomomorphismbiderivation |
| spellingShingle | Tae Hun Kim Ha Nuel Ju Hong Nyeong Kim Seong Yoon Jo Choonkil Park Bihomomorphisms and biderivations in Lie Banach algebras AIMS Mathematics hyers-ulam stability bi-additive s-functional inequality lie banach algebra bihomomorphism biderivation |
| title | Bihomomorphisms and biderivations in Lie Banach algebras |
| title_full | Bihomomorphisms and biderivations in Lie Banach algebras |
| title_fullStr | Bihomomorphisms and biderivations in Lie Banach algebras |
| title_full_unstemmed | Bihomomorphisms and biderivations in Lie Banach algebras |
| title_short | Bihomomorphisms and biderivations in Lie Banach algebras |
| title_sort | bihomomorphisms and biderivations in lie banach algebras |
| topic | hyers-ulam stability bi-additive s-functional inequality lie banach algebra bihomomorphism biderivation |
| url | https://www.aimspress.com/article/10.3934/math.2020145/fulltext.html |
| work_keys_str_mv | AT taehunkim bihomomorphismsandbiderivationsinliebanachalgebras AT hanuelju bihomomorphismsandbiderivationsinliebanachalgebras AT hongnyeongkim bihomomorphismsandbiderivationsinliebanachalgebras AT seongyoonjo bihomomorphismsandbiderivationsinliebanachalgebras AT choonkilpark bihomomorphismsandbiderivationsinliebanachalgebras |