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STABILITY OF DERIVATIONS ON PROPER LIE CQ*-ALGEBRAS

Najati, Abbas;Eskandani, G. Zamani

  • Published : 2009.01.31

Abstract

In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability for a following functional equation $$\sum\limits_{i=1}^mf(x_i+\frac{1}{m}\sum\limits_{{i=1\atop j{\neq}i}\.}^mx_j)+f(\frac{1}{m}\sum\limits_{i=1}^mx_i)=2f(\sum\limits_{i=1}^mx_i)$$ for a fixed positive integer m with $m\;{\geq}\;2$. This is applied to investigate derivations and their stability on proper Lie $CQ^*$-algebras. The concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.

Keywords

Hyers-Ulam-Rassias stability;proper Lie $CQ^*$-algebra;Lie derivation

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Cited by

  1. Hyers–Ulam–Rassias Stability of Derivations in Proper JCQ*–triples vol.10, pp.3, 2013, https://doi.org/10.1007/s00009-013-0248-2