Strong convergence theorems for the general split common fixed point problem in Hilbert spaces
-
1996
Downloads
-
3044
Views
Authors
Rudong Chen
- Department of Mathematics, Tian jin Polytechnic University, Tian jin 300387, China.
Tao Sun
- Department of Mathematics, Tian jin Polytechnic University, Tian jin 300387, China.
Huimin He
- School of Mathematics and Statistics, Xidian University, Xi'an 710071, China.
Jen-Chih Yao
- Center for General Education, China Medical University, Taichung 40402, Taiwan, ROC.
Abstract
In this paper, we propose and investigate a new iterative algorithm for solving the general split common fixed point problem in the setting of infinite-dimensional Hilbert spaces. We also prove the sequence generated by the proposed algorithm converge strongly to a common solution of the general split common fixed point problem. As application, some particular cases of directed operator and quasi-nonexpansive operator are also considered. Finally, we present several numerical results for general split common fixed point problem to demonstrate the efficiency of the proposed algorithm.
Share and Cite
ISRP Style
Rudong Chen, Tao Sun, Huimin He, Jen-Chih Yao, Strong convergence theorems for the general split common fixed point problem in Hilbert spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 10, 5433--5444
AMA Style
Chen Rudong, Sun Tao, He Huimin, Yao Jen-Chih, Strong convergence theorems for the general split common fixed point problem in Hilbert spaces. J. Nonlinear Sci. Appl. (2017); 10(10):5433--5444
Chicago/Turabian Style
Chen, Rudong, Sun, Tao, He, Huimin, Yao, Jen-Chih. "Strong convergence theorems for the general split common fixed point problem in Hilbert spaces." Journal of Nonlinear Sciences and Applications, 10, no. 10 (2017): 5433--5444
Keywords
- General split common fixed point problem
- demicontractive operator
- quasi-nonexpansive operator
- directed operator
MSC
References
-
[1]
C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems, 18 (2002), 441–453.
-
[2]
C. Byrne , A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2004), 103–120.
-
[3]
Y. Censor, T. Bortfeld, B. Martin, A. Trofimov , A unified approach for inversion problems in intensity-modulated radiation therapy , Phys. Med. Biol., 51 (2005), 2353–2365.
-
[4]
Y. Censor, Y. Elfving, A multiprojection algorithm using Bregman projections in a product space , Numer. Algorithms, 8 (1994), 221–239.
-
[5]
Y. Censor, Y. Elfving, N. Kopf, T. Bortfeld , The multiple-sets split feasibility problem and its applications for inverse problems, Inverse Problems, 21 (2005), 2071–2084.
-
[6]
Y. Censor, A. Segal, The split common fixed point problem for directed operators, J. Convex Anal., 16 (2009), 587–600.
-
[7]
R. D. Chen, Fixed point Theory and Applications, National Defence Industry Press, (2012)
-
[8]
P. L. Combettes, V. R.Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Model. Simul., 4 (2005), 1168–2000.
-
[9]
H.-H. Cui, F.-H. Wang, Iterative methods for the split common fixed point problem in Hilbert spaces, Fixed Point Theory Appl., 2014 (2014), 8 pages.
-
[10]
P. E. Maingé, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Anal., 16 (2008), 899–912.
-
[11]
A. Moudafi , The split common fixed point problem for demicontractive mappings, Inverse Problems, 26 (2010), 6 pages.
-
[12]
A. Moudafi, A note on the split common fixed-point problem for quasi-nonexpansive operators, Nonlinear Anal., 74 (2011), 4083–4087.
-
[13]
W. Takahashi, Nonlinear functional analysis, Fixed point theory and its applications, Yokohama Publishers, Yokohama (2000)
-
[14]
F.-H. Wang, H.-K. Xu , Cyclic algorithms for split feasibility problems in Hilbert spaces, Nonlinear Anal., 74 (2011), 4105–4111.
-
[15]
H.-K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), 240–256.
-
[16]
Y.-H. Yao, R. P. Agarwal, M. Postolache, Y.-C. Liou , Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem, Fixed Point Theory Appl., 2014 (2014), 14 pages.
-
[17]
Y.-H. Yao, M. Postolache, Y.-C. Liou , Strong convergence of a self-adaptive method for the split feasibility problem, Fixed Point Theory Appl., 2013 (2013), 12 pages.