A fixed point approach to the stability of quartic Lie $*$-derivations

Dongseung Kang, Heejeong Koh

Abstract


We obtain the general solution of the functional equation $f(ax+y)-f(x-ay)+\frac{1}{2}a(a^2+1)f(x-y)+(a^4-1)f(y)= \,\,\frac{1}{2}a(a^2+1)f(x+y)+(a^4-1)f(x)$ and prove the stability problem of the quartic Lie $*$-derivation by using a directed method and an alternative fixed point method.

Keywords


Hyers-Ulam stability; quartic mapping; Lie ∗-derivation; Banach ∗-algebra; fixed point alternative.

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References


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DOI: http://dx.doi.org/10.11568/kjm.2016.24.4.587

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