Korean J. Math. Vol. 24 No. 4 (2016) pp.587-600
DOI: https://doi.org/10.11568/kjm.2016.24.4.587

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

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Published: Dec 30, 2016
Keywords:
Hyers-Ulam stability, quartic mapping, Lie ∗-derivation, Banach ∗-algebra, fixed point alternative.
Mathematics Subject Classification:
Lie ∗-derivation, 39B55, Banach ∗-algebra, 39B72, 47B47, 47H10.

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Dongseung Kang
Mathematics Education Dankook University Yongin 16890, Korea
Heejeong Koh
Mathematics Education Dankook University Yongin 16890, Korea

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.


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