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

In: Approximation and Computation in Science and Engineering

Author

Listed:
  • Vahid Keshavarz

    (Shiraz University of Technology)

  • Sedigheh Jahedi

    (Shiraz University of Technology)

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 f ( x + y ) − f ( x ) − f ( y ) = ρ 2 f x + y 2 + f ( x ) + f ( y ) , f ( [ [ u , v ] , w ] ) = [ [ f ( u ) , f ( v ) ] , f ( w ) ] $$\displaystyle \begin{array}{@{}rcl@{}} \left \{ \begin {array}{ll} f(x+y)-f(x)-f(y)= \rho \left (2f\left (\frac {x+y}{2}\right )+ f(x)+ f(y)\right ),\\ f([[u,v],w])=[[f(u),f(v)],f(w)] \end {array} \right . \end{array} $$ in 3-Lie algebras where ρ≠1 is a fixed real number.

Suggested Citation

  • Vahid Keshavarz & Sedigheh Jahedi, 2022. "Hyperstability of Orthogonally 3-Lie Homomorphism: An Orthogonally Fixed Point Approach," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Approximation and Computation in Science and Engineering, pages 477-485, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-84122-5_25
    DOI: 10.1007/978-3-030-84122-5_25
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