Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 957541, 9 pages
doi:10.1155/2011/957541
Research Article

On the Stability of Quadratic Double Centralizers and Quadratic Multipliers: A Fixed Point Approach

Abasalt Bodaghi,1 Idham Arif Alias,2 and Madjid Eshaghi Gordji3

1Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran
2Laboratory of Theoretical Studies, Institute for Mathematical Research, University Putra Malaysia UPM, 43400 Serdang, Selangor Darul Ehsan, Malaysia
3Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran

Received 3 December 2010; Revised 11 January 2011; Accepted 18 January 2011

Academic Editor: Michel Chipot

Copyright © 2011 Abasalt Bodaghi 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 prove the superstability of quadratic double centralizers and of quadratic multipliers on Banach algebras by fixed point methods. These results show that we can remove the conditions of being weakly commutative and weakly without order which are used in the work of M. E. Gordji et al. (2011) for Banach algebras.