Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 181678, 10 pages
doi:10.1155/2009/181678
Research Article

Functional Equation f(x)=pf(x−1)−qf(x−2) and Its Hyers-Ulam Stability

Soon-Mo Jung

Mathematics Section, College of Science and Technology, Hongik University, Jochiwon 339-701, South Korea

Received 2 July 2009; Revised 30 September 2009; Accepted 5 November 2009

Academic Editor: László Losonczi

Copyright © 2009 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 solve the functional equation, f(x)=pf(x−1)−qf(x−2), and prove its Hyers-Ulam stability in the class of functions f:ℝ→X, where X is a real (or complex) Banach space.