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Journal of Function Spaces and Applications
Volume 2013, Article ID 237858, 8 pages
http://dx.doi.org/10.1155/2013/237858
Research Article

Generalized Virtually Stable Maps and Their Associated Sequences

1Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 18 April 2013; Accepted 8 June 2013

Academic Editor: Janusz Matkowski

Copyright © 2013 P. Chaoha 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

We extend the concept of virtual stability of continuous self-maps to arbitrary selfmaps and investigate the structure of sequences associated with uniformly virtually stable selfmaps. We also obtain a necessary and sufficient condition for a uniformly virtually stable selfmap to have the largest possible associated sequence. Examples of a uniformly virtually stable selfmap having the prescribed largest sequence and a uniformly virtually stable selfmap having no largest sequence are given.