- Research Article
- Open access
- Published:
Strong Convergence of Modified Implicit Iteration Processes for Common Fixed Points of Nonexpansive Mappings
Fixed Point Theory and Applications volume 2007, Article number: 048174 (2007)
Abstract
Strong convergence theorems are obtained by hybrid method for modified composite implicit iteration process of nonexpansive mappings in Hilbert spaces. The results presented in this paper generalize and improve the corresponding results of Nakajo and Takahashi (2003) and others.
References
Byrne C: A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Problems 2004,20(1):103–120. 10.1088/0266-5611/20/1/006
Podilchuk CI, Mammone RJ: Image recovery by convex projections using a least-squares constraint. Journal of the Optical Society of America A 1990,7(3):517–521. 10.1364/JOSAA.7.000517
Sezan MI, Stark H: Applications of convex projection theory to image recovery in tomography and related areas. In Image Recovery: Theory and Application. Edited by: Stark H. Academic Press, Orlando, Fla, USA; 1987:415–462.
Youla D: On deterministic convergence of iteration of relaxed projection operators. Journal of Visual Communication and Image Representation 1990,1(1):12–20. 10.1016/1047-3203(90)90013-L
Youla D: Mathematical theory of image restoration by the method of convex projections. In Image Recovery: Theory and Application. Edited by: Stark H. Academic Press, Orlando, Fla, USA; 1987:29–77.
Reich S: Weak convergence theorems for nonexpansive mappings in Banach spaces. Journal of Mathematical Analysis and Applications 1979,67(2):274–276. 10.1016/0022-247X(79)90024-6
Genel A, Lindenstrauss J: An example concerning fixed points. Israel Journal of Mathematics 1975,22(1):81–86. 10.1007/BF02757276
Nakajo K, Takahashi W: Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. Journal of Mathematical Analysis and Applications 2003,279(2):372–379. 10.1016/S0022-247X(02)00458-4
Xu H-K, Ori RG: An implicit iteration process for nonexpansive mappings. Numerical Functional Analysis and Optimization 2001,22(5–6):767–773. 10.1081/NFA-100105317
Osilike MO: Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps. Journal of Mathematical Analysis and Applications 2004,294(1):73–81. 10.1016/j.jmaa.2004.01.038
Martinez-Yanes C, Xu H-K: Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Analysis 2006,64(11):2400–2411. 10.1016/j.na.2005.08.018
Goebel K, Kirk WA: Topics in Metric Fixed Point Theory, Cambridge Studies in Advanced Mathematics. Volume 28. Cambridge University Press, Cambridge, UK; 1990:viii+244.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Zhang, F., Su, Y. Strong Convergence of Modified Implicit Iteration Processes for Common Fixed Points of Nonexpansive Mappings. Fixed Point Theory Appl 2007, 048174 (2007). https://doi.org/10.1155/2007/48174
Received:
Accepted:
Published:
DOI: https://doi.org/10.1155/2007/48174