Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 793947, 10 pages
doi:10.1155/2010/793947
Research Article

A Note on Stability of a Linear Functional Equation of Second Order Connected with the Fibonacci Numbers and Lucas Sequences

Janusz Brzdęk1 and Soon-Mo Jung2

1Department of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland
2Mathematics Section, College of Science and Technology, Hongik University, 339-701 Jochiwon, Republic of Korea

Received 26 April 2010; Accepted 15 July 2010

Academic Editor: Ram N. Mohapatra

Copyright © 2010 Janusz Brzdęk 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 prove the Hyers-Ulam stability of a second-order linear functional equation in single variable (with constant coefficients) that is connected with the Fibonacci numbers and Lucas sequences. In this way we complement, extend, and/or improve some recently published results on stability of that equation.