Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 872190, 11 pages
doi:10.1155/2008/872190
Stability of the Cauchy-Jensen Functional Equation in C∗-Algebras: A Fixed Point Approach
Choonkil Park1
and Jong Su An2
1Department of Mathematics, Hanyang University, Seoul 133-791, South Korea
2Department of Mathematics Education, Pusan National University, Pusan 609-735, South Korea
Abstract
we prove the Hyers-Ulam-Rassias stability of C∗-algebra homomorphisms and of generalized derivations on C∗-algebras for the following Cauchy-Jensen functional equation 2f((x+y)/2+z)=f(x)+f(y)+2f(z), which was introduced and investigated by Baak (2006). The concept of Hyers-Ulam-Rassias stability originated from the stability theorem of Th. M. Rassias that appeared in (1978).