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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 454569, 7 pages
Research Article

Hyers-Ulam Stability of Iterative Equation in the Class of Lipschitz Functions

Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China

Received 14 March 2014; Revised 10 May 2014; Accepted 10 May 2014; Published 1 June 2014

Academic Editor: Krzysztof Ciepliński

Copyright © 2014 Chao Xia and Wei Song. 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.


Hyers-Ulam stability is a basic sense of stability for functional equations. In the present paper we discuss the Hyers-Ulam stability of a kind of iterative equations in the class of Lipschitz functions. By the construction of a uniformly convergent sequence of functions we prove that, for every approximate solution of such an equation, there exists an exact solution near it.