Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 454093, 14 pages
doi:10.1155/2011/454093
Research Article

On Approximate 𝐶 ∗ -Ternary 𝑚 -Homomorphisms: A Fixed Point Approach

M. Eshaghi Gordji,1,2 Z. Alizadeh,1,2 Y. J. Cho,3 and H. Khodaei1,2

1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2Center of Excellence in Nonlinear Analysis and Applications (CENAA), Semnan University, Semnan, Iran
3Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea

Received 21 November 2010; Accepted 6 March 2011

Academic Editor: Jong Kim

Copyright © 2011 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

Using fixed point methods, we prove the stability and superstability of 𝐶 ∗ -ternary additive, quadratic, cubic, and quartic homomorphisms in 𝐶 ∗ -ternary rings for the functional equation 𝑓 ( 2 𝑥 + 𝑦 ) + 𝑓 ( 2 𝑥 − 𝑦 ) + ( 𝑚 − 1 ) ( 𝑚 − 2 ) ( 𝑚 − 3 ) 𝑓 ( 𝑦 ) = 2 𝑚 − 2 [ 𝑓 ( 𝑥 + 𝑦 ) + 𝑓 ( 𝑥 − 𝑦 ) + 6 𝑓 ( 𝑥 ) ] , for each 𝑚 = 1 , 2 , 3 , 4 .