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Hyperstability of Orthogonally 3-Lie Homomorphism: An Orthogonally Fixed Point Approach

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Approximation and Computation in Science and Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 180))

Abstract

In this chapter, by using the orthogonally fixed point method, we prove the Hyers–Ulam stability and the hyperstability of orthogonally 3-Lie homomorphisms for additive ρ-functional equation in 3-Lie algebras. Indeed, we investigate the stability and the hyperstability of the system of functional equations

$$\displaystyle \begin{array}{@{}rcl@{}} \left \{ \begin {array}{ll} f(x+y)-f(x)-f(y)= \rho \left (2f\left (\frac {x+y}{2}\right )+ f(x)+ f(y)\right ),\\ f([[u,v],w])=[[f(u),f(v)],f(w)] \end {array} \right . \end{array} $$

in 3-Lie algebras where ρ≠1 is a fixed real number.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Shiraz University of Technology, Shiraz, Iran

    Vahid Keshavarz & Sedigheh Jahedi

Authors
  1. Vahid Keshavarz
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  2. Sedigheh Jahedi
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Editors and Affiliations

  1. Department of Maths and Engineering Sciences, Hellenic Military Academy, Vari Attikis, Greece

    Nicholas J. Daras

  2. Department of Mathematics, Zografou Campus, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Keshavarz, V., Jahedi, S. (2022). Hyperstability of Orthogonally 3-Lie Homomorphism: An Orthogonally Fixed Point Approach. In: Daras, N.J., Rassias, T.M. (eds) Approximation and Computation in Science and Engineering. Springer Optimization and Its Applications, vol 180. Springer, Cham. https://doi.org/10.1007/978-3-030-84122-5_25

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