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arXiv · 2002.06441

Hyperstability of orthogonally 3-Lie homomorphism: an orthogonally fixed point approach

Vahid Keshavarz·Sedigheh Jahedi·Themistocles M. Rassias
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Abstract

In this paper, by using the orthogonally fixed point method, we prove the Hyers-Ulam stability and the hyperstability of orthogonally 3-Lie homomorphisms for additive $\rho$-functional equation in 3-Lie algebras.\\ Indeed, we investigate the Hyers-Ulam stability and the hyperstability of the system of functional equations \begin{eqnarray*} \left\{ \begin{array}{ll} f(x+y)-f(x)-f(y)= \rho(2f(\frac{x+y}{2})+ f(x)+ f(y)),\\ f([[x,y],z])=[[f(x),f(y)],f(z)] \end{array} \right. \end{eqnarray*} in 3-Lie algebras (where $\rho$ is a fixed real number with $\rho \ne 1$).

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Vahid Keshavarz, Sedigheh Jahedi, Themistocles M. Rassias. 2020-02-15. Hyperstability of orthogonally 3-Lie homomorphism: an orthogonally fixed point approach. https://arxiv.org/abs/2002.06441

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