Department of Mathematics, Beyza Branch, Islamic Azad University, Beyza, Iran.
Abstract
In this paper, using fixed point method, we prove the generalized Hyers-Ulam stability of random homomorphisms in random $C^*$-algebras and random Lie $C^*$-algebras and of derivations on Non-Archimedean random C$^*$-algebras and Non-Archimedean random Lie C$^*$-algebras for the following $m$-variable additive functional equation: $$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfleft( m x_i + sum_{j=1~,ineq j}^m x_jright)+fleft(sum_{i=1}^m x_iright) right]$$ The concept of Hyers-Ulam-Rassias stability originated from 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.
Azadi Kenary, H., Toorani, A., & Heidarzadegan, A. (2013). Fixed point approach to the Hyers-Ulam-Rassias approximation of homomorphisms and derivations on Non-Archimedean random Lie $C^*$-algebras. Caspian Journal of Mathematical Sciences, 2(1), 55-66.
MLA
H. Azadi Kenary; A. Toorani; A. Heidarzadegan. "Fixed point approach to the Hyers-Ulam-Rassias approximation of homomorphisms and derivations on Non-Archimedean random Lie $C^*$-algebras", Caspian Journal of Mathematical Sciences, 2, 1, 2013, 55-66.
HARVARD
Azadi Kenary, H., Toorani, A., Heidarzadegan, A. (2013). 'Fixed point approach to the Hyers-Ulam-Rassias approximation of homomorphisms and derivations on Non-Archimedean random Lie $C^*$-algebras', Caspian Journal of Mathematical Sciences, 2(1), pp. 55-66.
VANCOUVER
Azadi Kenary, H., Toorani, A., Heidarzadegan, A. Fixed point approach to the Hyers-Ulam-Rassias approximation of homomorphisms and derivations on Non-Archimedean random Lie $C^*$-algebras. Caspian Journal of Mathematical Sciences, 2013; 2(1): 55-66.
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