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

Vahid Keshavarz and Sedigheh Jahedi ()
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Vahid Keshavarz: Shiraz University of Technology
Sedigheh Jahedi: Shiraz University of Technology

A chapter in Approximation and Computation in Science and Engineering, 2022, pp 477-485 from Springer

Abstract: 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.

Keywords: Orthogonally fixed point method; Hyers–Ulam stability; 3-Lie homomorphism in orthogonally 3-Lie algebras; Hyperstability; Additive ρ-Jensen functional equation; Primary 46S10; 39B62; 39B52; 47H10; 12J25 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-84122-5_25

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DOI: 10.1007/978-3-030-84122-5_25

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