Multiple-set split feasibility problems for asymptotically strict pseudocontractions. (English) Zbl 1234.47047

Chang, Shih-Sen; Cho, Yeol Je; Kim, J. K.; Zhang, W. B.; Yang, L.

Abstr. Appl. Anal. 2012, Article ID 491760, 12 p. (2012).

Summary: We introduce an iterative method for solving the multiple-set split feasibility problems for asymptotically strict pseudocontractions in infinite-dimensional Hilbert spaces, and, by using the proposed iterative method, we improve and extend some recent results given by some authors.

MSC:

47J25	Iterative procedures involving nonlinear operators
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

References:

[1]	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. · Zbl 0828.65065
[2]	C. Byrne, “Iterative oblique projection onto convex sets and the split feasibility problem,” Inverse Problems, vol. 18, no. 2, pp. 441-453, 2002. · Zbl 0996.65048
[3]	Y. Censor, T. Bortfeld, B. Martin, and A. Trofimov, “A unified approach for inversion problems in intensity-modulated radiation therapy,” Physics in Medicine and Biology, vol. 51, no. 10, pp. 2353-2365, 2006.
[4]	Y. Censor, T. Elfving, N. Kopf, and T. Bortfeld, “The multiple-sets split feasibility problem and its applications for inverse problem and its applications,” Inverse Problems, vol. 21, no. 6, pp. 2071-2084, 2005. · Zbl 1089.65046
[5]	Y. Censor X, A. Motova, and A. Segal, “Perturbed projections and subgradient projections for the multiple-sets split feasibility problem,” Journal of Mathematical Analysis and Applications, vol. 327, no. 2, pp. 1244-1256, 2007. · Zbl 1253.90211
[6]	H. K. Xu, “A variable Krasnosel’skii-Mann algorithm and the multiple-set split feasibility problem,” Inverse Problems, vol. 22, no. 6, pp. 2021-2034, 2006. · Zbl 1126.47057
[7]	Q. Yang, “The relaxed CQ algorithm solving the split feasibility problem,” Inverse Problems, vol. 20, no. 4, pp. 1261-1266, 2004. · Zbl 1066.65047
[8]	J. Zhao and Q. Yang, “Several solution methods for the split feasibility problem,” Inverse Problems, vol. 21, no. 5, pp. 1791-1799, 2005. · Zbl 1080.65035
[9]	K. Goebel and W. A. Kirk, “A fixed point theorem for asymptotically nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 35, pp. 171-174, 1972. · Zbl 0256.47045
[10]	T. H. Kim and H. K. Xu, “Convergence of the modified Mann’s iteration method for asymptotically strict pseudo-contractions,” Nonlinear Analysis. Theory, Methods & Applications, vol. 68, no. 9, pp. 2828-2836, 2008. · Zbl 1220.47100
[11]	K. Aoyama, W. Kimura, W. Takahashi, and M. Toyoda, “Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space,” Nonlinear Analysis. Theory, Methods & Applications, vol. 67, no. 8, pp. 2350-2360, 2007. · Zbl 1130.47045
[12]	A. Moudafi, “The split common fixed-point problem for demicontractive mappings,” Inverse Problems, vol. 26, no. 5, Article ID 055007, 6 pages, 2010. · Zbl 1219.90185
[13]	H. K. Xu, “Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces,” Inverse Problems, vol. 26, no. 10, Article ID 105018, 17 pages, 2010. · Zbl 1213.65085
[14]	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. · Zbl 1189.65111
[15]	E. Masad and S. Reich, “A note on the multiple-set split convex feasibility problem in Hilbert space,” Journal of Nonlinear and Convex Analysis, vol. 8, no. 3, pp. 367-371, 2007. · Zbl 1171.90009