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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 560258, 9 pages
http://dx.doi.org/10.1155/2013/560258
Research Article

Fixed Point of a New Three-Step Iteration Algorithm under Contractive-Like Operators over Normed Spaces

1Department of Mathematical Engineering, Faculty of Chemistry-Metallurgical, Yildiz Technical University, Davutpasa Campus, Esenler, 34210 Istanbul, Turkey
2Department of Mathematics, Faculty of Science and Letters, Yildiz Technical University, Davutpasa Campus, Esenler, 34220 Istanbul, Turkey

Received 2 September 2013; Accepted 14 October 2013

Academic Editor: S. A. Mohiuddine

Copyright © 2013 Vatan Karakaya 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 introduce a new three-step iteration scheme and prove that this new iteration scheme is convergent to fixed points of contractive-like operators. Also, by providing an example, we show that our new iteration method is faster than another iteration method due to Suantai (2005). Furthermore, it is shown that this new iteration method is equivalent to some other iteration methods in the sense of convergence. Finally, it is proved that this new iteration method is -stable.