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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 386930, 5 pages
Inertial Iteration for Split Common Fixed-Point Problem for Quasi-Nonexpansive Operators
1School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China
2College of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454000, China
Received 14 March 2013; Accepted 6 May 2013
Academic Editor: Ru Dong Chen
Copyright © 2013 Yazheng Dang and Yan Gao. 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.
- J. W. Chinneck, “The constraint consensus method for finding approximately feasible points in nonlinear programs,” INFORMS Journal on Computing, vol. 16, no. 3, pp. 255–265, 2004.
- F. Deutsch, “The method of alternating orthogonal projections,” in Approximation Theory, Spline Functions and Applications, vol. 356 of NATO Advanced Science Institutes Series C, pp. 105–121, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992.
- Y. Censor, “Parallel application of block-iterative methods in medical imaging and radiation therapy,” Mathematical Programming, vol. 42, no. 2, pp. 307–325, 1988.
- G. T. Herman, Image Reconstruction from Projections: The Fundamentals of Computerized Tomography, Academic Press, New York, NY, USA, 1980.
- Y. Gao, “Determining the viability for a affine nonlinear control system,” Journal of Control Theory & Applications, vol. 26, no. 6, pp. 654–656, 2009 (Chinese).
- Y. Censor and T. Elfving, “A multiprojection algorithm using Bregman projections in a product space,” Numerical Algorithms, vol. 8, no. 2–4, pp. 221–239, 1994.
- Y. Dang and Y. Gao, “The strong convergence of a KM-CQ-like algorithm for a split feasibility problem,” Inverse Problems, vol. 27, no. 1, Article ID 015007, 2011.
- P.-E. Maingé, “Convergence theorems for inertial KM-type algorithms,” Journal of Computational and Applied Mathematics, vol. 219, no. 1, pp. 223–236, 2008.
- B. Qu and N. Xiu, “A note on the algorithm for the split feasibility problem,” Inverse Problems, vol. 21, no. 5, pp. 1655–1665, 2005.
- C. Byrne, “Iterative oblique projection onto convex sets and the split feasibility problem,” Inverse Problems, vol. 18, no. 2, pp. 441–453, 2002.
- Y. Censor and A. Segal, “The split common fixed point problem for directed operators,” Journal of Convex Analysis, vol. 16, no. 2, pp. 587–600, 2009.
- Y. Dang, Y. Gao, and Y. Han, “A perturbed projection algorithm with inertial technique for split feasibility problem,” Journal of Applied Mathematics, vol. 2012, Article ID 207323, 10 pages, 2012.
- S. Măruşter and C. Popirlan, “On the Mann-type iteration and the convex feasibility problem,” Journal of Computational and Applied Mathematics, vol. 212, no. 2, pp. 390–396, 2008.
- H. H. Bauschke and P. L. Combettes, “A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces,” Mathematics of Operations Research, vol. 26, no. 2, pp. 248–264, 2001.
- A. Moudafi, “A note on the split common fixed-point problem for quasi-nonexpansive operators,” Nonlinear Analysis, vol. 74, no. 12, pp. 4083–4087, 2011.
- Z. Opial, “Weak convergence of the sequence of successive approximations for nonexpansive mappings,” Bulletin of the American Mathematical Society, vol. 73, pp. 591–597, 1967.