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)+(n2)i=1nf(xi)=1i<jnf(xixj) when n>2. We prove the general solutions and investigate its generalized Ulam-Gavruta-Rassias stability.