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<p>In this paper, we establish the general solution of a certain class of functional equations associated with the Jordan–von Neumann identity. Applications in connection with asymptotic behaviors of quadratic <i>n</i>-Jordan <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(^*\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∗</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>-derivations on Banach <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(^*\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∗</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>-algebras are provided. In consequence, the behavior of perturbations of quadratic Jordan <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(^*\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∗</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>-derivations and quadratic mappings is also treated.</p>

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On the Approximate Behavior of Quadratic n-Jordan \(^*\)-Derivations

  • 期刊论文

  • 发表日期：

    2026年1月3日

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  • Hamid Khodaei

摘要

In this paper, we establish the general solution of a certain class of functional equations associated with the Jordan–von Neumann identity. Applications in connection with asymptotic behaviors of quadratic n-Jordan \(^*\) ∗ -derivations on Banach \(^*\) ∗ -algebras are provided. In consequence, the behavior of perturbations of quadratic Jordan \(^*\) ∗ -derivations and quadratic mappings is also treated.