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Journal of Function Spaces
Volume 2016, Article ID 8164978, 6 pages
http://dx.doi.org/10.1155/2016/8164978
Research Article

On the Hyers-Ulam Stability of First-Order Impulsive Delay Differential Equations

1Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
2Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

Received 10 December 2015; Revised 12 February 2016; Accepted 23 February 2016

Academic Editor: Janusz Brzdęk

Copyright © 2016 Akbar Zada et al. 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

This paper proves the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of nonlinear first-order ordinary differential equation with single constant delay and finite impulses on a compact interval. Our approach uses abstract Gronwall lemma together with integral inequality of Gronwall type for piecewise continuous functions.