International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 63239, 10 pages
doi:10.1155/2007/63239
Research Article
On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations
Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
Received 18 April 2007; Revised 22 April 2007; Accepted 23 April 2007
Academic Editor: Martin J. Bohner
Copyright © 2007 Paisan Nakmahachalasint. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.