Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 128479, 15 pages
http://dx.doi.org/10.1155/2011/128479
Research Article

The Stability of Some Differential Equations

M. M. Pourpasha,1 Th. M. Rassias,2 R. Saadati,3 and S. M. Vaezpour4

1Department of Mathematics, Chalous Branch, Islamic Azad University (IAU), Chalous 46615, Iran
2Department of Mathematics, National Technical University of Athens, Zografou Campus, 157 80 Athens, Greece
3Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran 14778, Iran
4Department of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Ave., Tehran, Iran

Received 17 October 2011; Accepted 17 November 2011

Academic Editor: Alexander P. Seyranian

Copyright © 2011 M. M. Pourpasha 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 generalize the results obtained by Jun and Min (2009) and use fixed point method to obtain the stability of the functional equation 𝑓 ( 𝑥 + 𝜎 ( 𝑦 ) ) = 𝐹 [ 𝑓 ( 𝑥 ) , 𝑓 ( 𝑦 ) ] , for a class of functions of a vector space into a Banach space where 𝜎 is an involution. Then we obtain the stability of the differential equations of the form 𝑦 = 𝐹 [ 𝑞 ( 𝑥 ) , 𝑃 ( 𝑥 ) 𝑦 ( 𝑥 ) ] .