Guo, Fengjun; Kang, Shin Min; Kwun, Young Chel An implicit algorithm for the split fixed point and convex feasibility problems. (English) Zbl 1470.65116 Abstr. Appl. Anal. 2013, Article ID 854893, 7 p. (2013). Summary: We consider an implicit algorithm for the split fixed point and convex feasibility problems. Strong convergence theorem is obtained. MSC: 65J22 Numerical solution to inverse problems in abstract spaces 47J25 Iterative procedures involving nonlinear operators 65F10 Iterative numerical methods for linear systems 65K10 Numerical optimization and variational techniques 90C25 Convex programming PDF BibTeX XML Cite \textit{F. Guo} et al., Abstr. Appl. Anal. 2013, Article ID 854893, 7 p. (2013; Zbl 1470.65116) Full Text: DOI References: [1] Censor, Y.; Bortfeld, T.; Martin, B.; Trofimov, A., A unified approach for inversion problems in intensity modulated radiation therapy, Physics in Medicine and Biology, 51, 2353-2365 (2006) [2] Yao, Y.; Jigang, W.; Liou, Y.-C., Regularized methods for the split feasibility problem, Abstract and Applied Analysis, 2012 (2012) · Zbl 1235.94028 [3] Ceng, L.-C.; Ansari, Q. H.; Yao, J.-C., Relaxed extragradient methods for finding minimum-norm solutions of the split feasibility problem, Nonlinear Analysis. Theory, Methods & Applications, 75, 4, 2116-2125 (2012) · Zbl 1236.47066 [4] Ceng, L.-C.; Ansari, Q. H.; Yao, J.-C., Mann type iterative methods for finding a common solution of split feasibility and fixed point problems, Positivity, 16, 3, 471-495 (2012) · Zbl 1336.65100 [5] Xu, H.-K., A variable Krasnosel’skii-Mann algorithm and the multiple-set split feasibility problem, Inverse Problems, 22, 6, 2021-2034 (2006) · Zbl 1126.47057 [6] Yao, Y.; Kim, T. H.; Chebbi, S.; Xu, H. K., A modified extragradient method for the split feasibility and fixed point problems, Journal of Nonlinear and Convex Analysis, 13, 383-396 (2012) · Zbl 1283.47067 [7] Censor, Y.; Elfving, T., A multiprojection algorithm using Bregman projections in a product space, Numerical Algorithms, 8, 2-4, 221-239 (1994) · Zbl 0828.65065 [8] Byrne, C., Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems, 18, 2, 441-453 (2002) · Zbl 0996.65048 [9] Dang, Y.; Gao, Y., The strong convergence of a KM-CQ-like algorithm for a split feasibility problem, Inverse Problems, 27, 1 (2011) · Zbl 1211.65065 [10] Zhao, J.; Yang, Q., Several solution methods for the split feasibility problem, Inverse Problems, 21, 5, 1791-1799 (2005) · Zbl 1080.65035 [11] Yang, Q., The relaxed CQ algorithm solving the split feasibility problem, Inverse Problems, 20, 4, 1261-1266 (2004) · Zbl 1066.65047 [12] Xu, H.-K., Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces, Inverse Problems, 26, 10 (2010) · Zbl 1213.65085 [13] Ceng, L.-C.; Ansari, Q. H.; Yao, J.-C., An extragradient method for solving split feasibility and fixed point problems, Computers & Mathematics with Applications, 64, 4, 633-642 (2012) · Zbl 1252.65102 [14] Goebel, K.; Kirk, W. A., Topics in Metric Fixed Point Theory. Topics in Metric Fixed Point Theory, Cambridge Studies in Advanced Mathematics, 28 (1990), Cambridge University Press · Zbl 0708.47031 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.