Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 210340, 14 pages
doi:10.1155/2010/210340
Research Article

Degree of Convergence of Iterative Algorithms for Boundedly Lipschitzian Strong Pseudocontractions

Songnian He,1,2 Yongfu Su,3 and Ronghua Li1

1College of Science, Civil Aviation University of China, Tianjin 300300, China
2Tianjin Key Laboratory for Advanced Signal Processing, Civil Aviation University of China, Tianjin 300300, China
3Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China

Received 25 September 2010; Accepted 19 December 2010

Academic Editor: Satit Saejung

Copyright © 2010 Songnian He 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

Let 𝐶 be a nonempty closed convex subset of a real Hilbert space 𝐻 , and let 𝑇 ∶ 𝐶 → 𝐻 be a boundedly Lipschitzian strong pseudo-contraction with a nonempty fixed point set. Three iterative algorithms are proposed for approximating the unique fixed point of 𝑇 ; one of them is for the self-mapping case, and the others are for the nonself-mapping case. Not only the strong convergence, but also the degree of convergence of the three iterative algorithms is obtained. Some numerical results corresponding to the self-mapping case are given which show advantages of our methods. As an application of our results, adopting the regularization idea, we also propose implicit and explicit algorithms for approximating a fixed point of a boundedly Lipschitzian pseudocontractive self-mapping from 𝐶 into itself, respectively.