Abstract and Applied Analysis
Volume 2012 (2012), Article ID 926390, 23 pages
http://dx.doi.org/10.1155/2012/926390
Research Article

On the Hyers-Ulam Stability of a General Mixed Additive and Cubic Functional Equation in n-Banach Spaces

Tian Zhou Xu1 and John Michael Rassias2

1School of Mathematics, Beijing Institute of Technology, Beijing 100081, China
2Pedagogical Department E.E., Section of Mathematics and Informatics, National and Kapodistrian University of Athens, 4 Agamemnonos Street, Aghia Paraskevi, Athens 15342, Greece

Received 7 January 2012; Accepted 15 February 2012

Academic Editor: Krzysztof Cieplinski

Copyright © 2012 Tian Zhou Xu and John Michael Rassias. 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

The objective of the present paper is to determine the generalized Hyers-Ulam stability of the mixed additive-cubic functional equation in n-Banach spaces by the direct method. In addition, we show under some suitable conditions that an approximately mixed additive-cubic function can be approximated by a mixed additive and cubic mapping.