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Journal of Function Spaces
Volume 2016 (2016), Article ID 6078298, 6 pages
http://dx.doi.org/10.1155/2016/6078298
Research Article

On the Hyers-Ulam Stability of the First-Order Difference Equation

Mathematics Section, College of Science and Technology, Hongik University, Sejong 30016, Republic of Korea

Received 25 May 2016; Accepted 10 July 2016

Academic Editor: Jaeyoung Chung

Copyright © 2016 Soon-Mo Jung and Young Woo Nam. 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 Hyers-Ulam stability of the first-order difference equation of the form , where is a given function with some moderate features. Moreover, we introduce some conditions for the function under which the difference equation is not stable in the sense of Hyers and Ulam.