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http://dx.doi.org/10.4134/CKMS.2009.24.1.005

STABILITY OF DERIVATIONS ON PROPER LIE CQ*-ALGEBRAS  

Najati, Abbas (DEPARTMENT OF MATHEMATICS FACULTY SCIENCES UNIVERSITY OF MOHAGHEGH ARDABILI)
Eskandani, G. Zamani (FACULTY OF MATHEMATICAL SCIENCES UNIVERSITY OF TABRIZ)
Publication Information
Communications of the Korean Mathematical Society / v.24, no.1, 2009 , pp. 5-16 More about this Journal
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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