Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 961642, 10 pages
http://dx.doi.org/10.1155/2012/961642
Research Article

Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras

Madjid Eshaghi Gordji,1 Badrkhan Alizadeh,2 Young Whan Lee,3 and Gwang Hui Kim4

1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2Technical and Vocational University of Iran, Technical and Vocational Faculty of Tabriz, P.O. Box 51745-135, Tabriz, Iran
3Department of Computer Hacking and Information Security, Daejeon University, Dong-gu, Daejeon 300-716, Republic of Korea
4Department of Mathematics, Kangnam University, Yongin, Gyeonggi 446-702, Republic of Korea

Received 27 January 2012; Revised 18 March 2012; Accepted 19 March 2012

Academic Editor: John Rassias

Copyright © 2012 Madjid 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

Let 𝑛 > 1 be an integer, let 𝐴 be an algebra, and 𝑋 be an 𝐴 -module. A quadratic function 𝐷 ∶ 𝐴 → 𝑋 is called a quadratic 𝑛 -derivation if ∏ 𝐷 ( 𝑛 𝑖 = 1 𝑎 𝑖 ) = 𝐷 ( 𝑎 1 ) 𝑎 2 2 ⋯ 𝑎 2 𝑛 + 𝑎 2 1 𝐷 ( 𝑎 2 ) 𝑎 2 3 ⋯ 𝑎 2 𝑛 + ⋯ + 𝑎 2 1 𝑎 2 2 ⋯ 𝑎 2 𝑛 − 1 𝐷 ( 𝑎 𝑛 ) for all 𝑎 1 ,..., 𝑎 𝑛 ∈ 𝐴 . We investigate the Hyers-Ulam stability of quadratic 𝑛 -derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.