Convergence Analysis of Two Demicontractive Operators
In this paper, first we introduce a new iterative scheme involving demicontractive mappings in Hilbert spaces which does not require prior knowledge of operator norm and, second, by using the proposed scheme, prove some strong convergence theorems. Finally, we give some numerical examples to illustrate our main result.
C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problem 18 (2004), 103 – 120, PII: S0266-5611(04)68668-0.
A. Cegielski, General method for solving the split common fixed point problem, J. Optim Theory Appl. 165 (2015), 385 – 404, DOI: 10.1007/s10957-014-0662-z.
Y. Censor and A. Segal, The split common fixed point problem for directed operators, J. Convex Anal. 16(2) (2009), 587 – 600, DOI: 10.1088/0266-5611/26/5/055007.
Y. Censor and T. Elfving, A multi projection algorithms using Bregman projection in a product space, Numer. Algorithms 8 (1994), 221 – 239, DOI: 10.1007/BF02142692.
Y. Censor, A. Gibali and S. Reich, Algorithms for the split variational inequality problem, Numer. Algorithms 59 (2012), 301 – 323, DOI: 10.1007/s11075-011-9490-5.
Y. Censor, T. Bortfeld, B. Martin and A. Trofimov, A unified approach for inversion problems in intensity-modulated radiation therapy, Phys. Med. Biol. 51 (2006), 2353 – 2365, DOI: 10.1088/0031-9155/51/10/001.
H. Cui and F. Wang, Iterative methods for the split common fixed point problem in a Hilbert space, Fixed Point Theory Appl. 2014 (2014), 78, DOI: 10.1186/1687-1812-2014-78.
M. Eslamian, General algorithms for split common fixed point problem of demicontractive mappings, Optimization, Optimization 65(2) (2016), 443-465 , DOI: 10.1080/02331934.2015.1053883.
A. Moudafi, A note on the split common fixed-point problem for quasi-nonexpansive operators, Nonlinear Anal. 74 (2011), 4083 – 4087, DOI: 10.1016/j.na.2011.03.041.
A. Moudafi, The split common fixed-point problem for demicontractive mappings, Inverse Problem 26 (2010), 587 – 600, DOI: 10.1088/0266-5611/26/5/055007.
A. Padcharoen, P. Kumam and Y. J. Cho, Split common fixed point problems for demicontractive operators, Numerical Algorithms (2018), 1 – 24, DOI: 10.1007/s11075-018-0605-0.
B. Qu and N. Xiu, A note on the CQ algorithm for the split feasibility problem, Inverse Probl. 21(5) (2005), 1655 – 1665, DOI: 10.1088/0266-5611/21/5/009.
Y. Shehu and P. Cholamjiak, Another look at the split common fixed point problem for demicontractive operators, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas 110 (2016), 201 – 218, DOI: 10.1007/s13398-015-0231-9.
S. Suantai, N. Pholasa and P. Cholamjiak, Relaxed CQ algorithms involving the inertial technique for multiple-sets split feasibility problems, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas 113(2) (2018), 1 – 19, DOI: 10.1007/s13398-018-0535-7.
S. Suantai, N. Pholasa and P. Cholamjiak, The modified inertial relaxed CQ algorithm for solving the split feasibility problems, J. Indust. Manag. Optim. 14(4) (2018), 1595 – 1615, DOI: 10.3934/jimo.2018023.
S. Suantai, Y. Shehu, P. Cholamjiak and O. S. Iyiola, Strong convergence of a self-adaptive method for the split feasibility problem in Banach spaces, J. Fixed Point Theory Appl. 20(2) (2018), 1595 – 1615, DOI: 10.1007/s11784-018-0549-y.
Y. C. Tang, J. G. Peng and L. W. Liu, A cyclic algorithm for the split common fixed point problem of demicontractive mappings in Hilbert spaces, Math. Model. Anal. 17 (2012), 457 – 466, DOI: 10.3846/13926292.2012.706236.
N. T. Vinh, P. Cholamjiak and S. Suantai, A new CQ algorithm for solving split feasibility problems in Hilbert spaces, Bull. Malays. Math. Sci. Soc. (2018), 1 – 18, DOI: 10.1007/s40840-018-0614-0.
F. Wang, A new iterative method for the split common fixed point problem in Hilbert spaces, Optimization 66 (2017), 407 – 415, DOI: 10.1080/02331934.2016.1274991.
H. K. Xu, Iterative algorithm for nonlinear operators, J. Lond. Math. Soc. 66 (2002), 1 – 17, DOI: 10.1112/S0024610702003332.
Y. Yao and Y. J. Cho, A strong convergence of a modified Krasnoselskii-Mann method for nonexpansive mappings in Hilbert spaces, Math. Model. Anal. 15 (2010), 265 – 274, DOI: 10.3846/1392-6292.2010.15.265-274.
Y. Yao, L. Leng, M. Postolache and X. Zheng, A unified framework for the two-sets split common fixed point problem in Hilbert spaces, J. Nonlinear Sci. Appl. 9(12) (2016), 6113 – 6125.
Y. Yao, L. Leng, M. Postolache and X. Zheng, Mann-type iteration method for solving the split common fixed point problem, J. Nonlinear Convex Anal. 18(5) (2017), 875 – 882, DOI: 10.1186/1687-1812-2014-183.
Y. Yao, R. P. Agarwal, M. Postolache and Y. C. Liu, Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem, Fixed Point Theory Appl. 2014 (2014), Article ID 183, DOI: 10.1186/1687-1812-2014-183.
Y. Yao, Y. C. Liou and M. Postolache, Self-adaptive algorithms for the split problem of the demicontractive operators, Optimization 67 (2018), 1309 – 1319, DOI: 10.1080/02331934.2017.1390747.
J. Zhao and S. He, Strong convergence of the viscosity approximation process for the split common fixed point problem of quasi-nonexpansive mappings, J. Appl. Math. 2012 (2012), Article ID 438023, 12 pages, DOI: 10.1155/2012/438023.
J. Zho, Solving split equality fixed-point problem of quasi-nonexpansive mappings without prior knowledge of operators norms, Optimization 64(12) (2015), 2619 – 2630, DOI: 10.1080/02331934.2014.883515.
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