Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 743032, 8 pages
http://dx.doi.org/10.1155/2014/743032
Research Article

Local Stability for Iterative Roots of Orientation-Preserving Self-Mappings on the Interval

Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China

Received 9 April 2014; Accepted 1 May 2014; Published 21 May 2014

Academic Editor: Yongkun Li

Copyright © 2014 Yingying Zeng. 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

Stability of iterative roots is important in their numerical computation. It is known that under some conditions iterative roots of orientation-preserving self-mappings are both globally stable and locally stable but globally unstable. Although the global instability implies the general global ( ) instability, the local stability does not guarantee the local ( ) stability. In this paper we generally prove the local ( ) stability for iterative roots. For this purpose we need a uniform estimate for the approximation to the conjugation in linearization, which is given by improving the method used for the case.