Advances in Difference Equations
Volume 2009 (2009), Article ID 273165, 22 pages
doi:10.1155/2009/273165
Stability of a Generalized Euler-Lagrange Type Additive Mapping and Homomorphisms in C∗-Algebras
Abbas Najati1
and Choonkil Park2
1Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, 56199-11367, Iran
2Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul, 133-791, South Korea
Abstract
Let X,Y be Banach modules over a C∗-algebra and let r1,…,rn∈ℝ be given. We prove the generalized Hyers-Ulam stability of the following functional equation in Banach modules over a unital C∗-algebra: ∑j=1nf(−rjxj+∑1≤i≤n,i≠jrixi)+2∑i=1nrif(xi)=nf(∑i=1nrixi). We show that if ∑i=1nri≠0, ri,rj≠0 for some 1≤i<j≤n and a mapping f:X→Y satisfies the functional equation mentioned above then the mapping f:X→Y is Cauchy additive. As an application, we investigate homomorphisms in unital C∗-algebras.