STABILITY OF DERIVATIONS ON PROPER LIE CQ*-ALGEBRAS

Title & Authors
STABILITY OF DERIVATIONS ON PROPER LIE CQ*-ALGEBRAS
Najati, Abbas; Eskandani, G. Zamani;

Abstract
In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability for a following functional equation $\small{\sum\limits_{i=1}^mf(x_i+\frac{1}{m}\sum\limits_{{i=1\atop j{\neq}i}\.}^mx_j)+f(\frac{1}{m}\sum\limits_{i=1}^mx_i)=2f(\sum\limits_{i=1}^mx_i)}$ for a fixed positive integer m with $\small{m\;{\geq}\;2}$. This is applied to investigate derivations and their stability on proper Lie $\small{CQ^*}$-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 $\small{CQ^*}$-algebra;Lie derivation;
Language
English
Cited by
1.
Hyers–Ulam–Rassias Stability of Derivations in Proper JCQ*–triples, Mediterranean Journal of Mathematics, 2013, 10, 3, 1391
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