Abstract and Applied Analysis
Volume 2011 (2011), Article ID 602713, 15 pages
http://dx.doi.org/10.1155/2011/602713
Research Article

A Note on Stability of an Operator Linear Equation of the Second Order

Janusz Brzdȩk1 and Soon-Mo Jung2

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

Received 3 April 2011; Accepted 7 June 2011

Academic Editor: Dumitru Baleanu

Copyright © 2011 Janusz Brzdȩk 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 some Hyers-Ulam stability results for an operator linear equation of the second order that is patterned on the difference equation, which defines the Lucas sequences (and in particular the Fibonacci numbers). In this way, we obtain several results on stability of some linear functional and differential and integral equations of the second order and some fixed point results for a particular (not necessarily linear) operator.