Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 162371, 11 pages
doi:10.1155/2010/162371
Research Article

Generalized Hyers-Ulam-Rassias Theorem in Menger Probabilistic Normed Spaces

M. Eshaghi Gordji,1 M. B. Ghaemi,2 and H. Majani2

1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

Received 24 September 2009; Accepted 22 January 2010

Academic Editor: Yong Zhou

Copyright © 2010 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 introduce two reasonable versions of approximately additive functions in a Šerstnev probabilistic normed space endowed with ΠM triangle function. More precisely, we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in above mentioned spaces.