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<p>In this article, by using the concept of Jensen and additive mappings, we define the Jensen <i>ρ</i>-functional equation which preserves orthogonality, where <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3324_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>ρ</mi> <mo>≠</mo> <mn>0</mn> <mo>,</mo> <mo>±</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$\rho \neq 0, \pm 1$</EquationSource> </InlineEquation>, and we show it to be orthogonally additive. Also, we investigate it as an orthogonal <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3324_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">C</mi> </math></EquationSource> <EquationSource Format="TEX">$\mathbb{C}$</EquationSource> </InlineEquation>-linear mapping between orthogonal normed spaces. In the following, we introduce orthogonal generalized triple Lie bracket (triple) derivation-derivations on orthogonal triple Banach algebras. Finally, by employing the fixed point methods, we show that the orthogonal generalized triple Lie bracket (triple) derivation-derivations on orthogonal triple Banach algebras can be Hyers–Ulam stable and hyperstable.</p>

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Orthogonal generalized Lie bracket of triple derivations: properties and stability

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月9日

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  • Zohreh Kefayati,
  • Thabet Abdeljawad,
  • Aiman Mukheimer,
  • Manar A. Alqudah

摘要

In this article, by using the concept of Jensen and additive mappings, we define the Jensen ρ-functional equation which preserves orthogonality, where ρ ≠ 0 , ± 1 $\rho \neq 0, \pm 1$ , and we show it to be orthogonally additive. Also, we investigate it as an orthogonal C $\mathbb{C}$ -linear mapping between orthogonal normed spaces. In the following, we introduce orthogonal generalized triple Lie bracket (triple) derivation-derivations on orthogonal triple Banach algebras. Finally, by employing the fixed point methods, we show that the orthogonal generalized triple Lie bracket (triple) derivation-derivations on orthogonal triple Banach algebras can be Hyers–Ulam stable and hyperstable.