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Journal of Function Spaces
Volume 2014, Article ID 398673, 6 pages
http://dx.doi.org/10.1155/2014/398673
Research Article

Hyers-Ulam Stability of Differentiation Operator on Hilbert Spaces of Entire Functions

1School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
2Department of Mathematics, Changzhi University, Changzhi, Shanxi 046011, China

Received 15 April 2014; Accepted 16 June 2014; Published 6 July 2014

Academic Editor: Zbigniew Leśniak

Copyright © 2014 Chun Wang and Tian-Zhou Xu. 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 investigate the Hyers-Ulam stability of differentiation operator on Hilbert spaces of entire functions. We give a necessary and sufficient condition in order that the operator has the Hyers-Ulam stability and also show that the best constant of Hyers-Ulam stability exists.