On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations

doi:10.1155/2007/63239

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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

Paisan Nakmahachalasint

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.