International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 63239, 10 pages
doi:10.1155/2007/63239

On the generalized Ulam-Gavruta-Rassias stability of mixed-type linear and Euler-Lagrange-Rassias functional equations

Abstract

In this paper, the mixed-type linear and Euler-Lagrange-Rassias functional equations introduced by J. M. Rassias is generalized to the following n-dimensional functional equation: f(∑i=1nxi)+(n−2)∑i=1nf(xi)=∑1≤i<j≤nf(xi−xj) when n>2. We prove the general solutions and investigate its generalized Ulam-Gavruta-Rassias stability.