Abstract and Applied Analysis
Volume 2012 (2012), Article ID 984160, 10 pages
http://dx.doi.org/10.1155/2012/984160
Research Article

Approximately Ternary Homomorphisms and Derivations on 𝐶 ∗ -Ternary Algebras

M. Eshaghi Gordji,1 A. Ebadian,2 N. Ghobadipour,3 J. M. Rassias,4 and M. B. Savadkouhi5

1Department of Mathematics, Semnan University, Semnan 35195-363, Iran
2Department of Mathematics, Payame Noor University, Tabriz Branch, Tabriz, Iran
3Department of Mathematics, Urmia University, Urmia, Iran
4Section of Mathematics and Informatics, Pedagogical Department, National and Kapodistrian University of Athens, 4, Agamemnonos Street, Aghia Paraskevi, 15342 Athens, Greece
5Department of Mathematics, Islamic Azad University, Mahdishahr Branch, Mahdishahr, Semnan, Iran

Received 4 December 2011; Accepted 17 January 2012

Academic Editor: Josip E. Pecaric

Copyright © 2012 M. Eshaghi Gordji et al. 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

We investigate the stability and superstability of ternary homomorphisms between 𝐶 ∗ -ternary algebras and derivations on 𝐶 ∗ -ternary algebras, associated with the following functional equation 𝑓 ( ( 𝑥 2 − 𝑥 1 ) / 3 ) + 𝑓 ( ( 𝑥 1 − 3 𝑥 3 ) / 3 ) + 𝑓 ( ( 3 𝑥 1 + 3 𝑥 3 − 𝑥 2 ) / 3 ) = 𝑓 ( 𝑥 1 ) .