Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 503458, 10 pages
doi:10.1155/2010/503458
Research Article

Approximately Quadratic Mappings on Restricted Domains

Abbas Najati1 and Soon-Mo Jung2

1Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran
2Mathematics Section, College of Science and Technology, Hongik University, Jochiwon 339-701, Republic of Korea

Received 16 September 2010; Accepted 20 December 2010

Academic Editor: Andrei Volodin

Copyright © 2010 Abbas Najati and Soon-Mo Jung. 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 a generalized quadratic functional equation 𝑓 ( 𝑟 𝑥 + 𝑠 𝑦 ) = 𝑟 𝑓 ( 𝑥 ) + 𝑠 𝑓 ( 𝑦 ) − 𝑟 𝑠 𝑓 ( 𝑥 − 𝑦 ) , where 𝑟 , 𝑠 are nonzero real numbers with 𝑟 + 𝑠 = 1 . We show that this functional equation is quadratic if 𝑟 , 𝑠 are rational numbers. We also investigate its stability problem on restricted domains. These results are applied to study of an asymptotic behavior of these generalized quadratic mappings.