Research article

Bihomomorphisms and biderivations in Lie Banach algebras

  • Received: 04 October 2019 Accepted: 25 February 2020 Published: 27 February 2020
  • MSC : 39B52, 47B47, 39B62, 17B40

  • In this paper, we solve the following bi-additive $s$-functional inequality $ \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)} \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}~~~~~~\left( {0.1} \right) $ where $s$ is a fixed nonzero complex number satisfying $|s| \lt 1$. 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).

    Citation: Tae Hun Kim, Ha Nuel Ju, Hong Nyeong Kim, Seong Yoon Jo, Choonkil Park. Bihomomorphisms and biderivations in Lie Banach algebras[J]. AIMS Mathematics, 2020, 5(3): 2196-2210. doi: 10.3934/math.2020145

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  • In this paper, we solve the following bi-additive $s$-functional inequality $ \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)} \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}~~~~~~\left( {0.1} \right) $ where $s$ is a fixed nonzero complex number satisfying $|s| \lt 1$. 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).


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