Split feasibility problem for quasi-nonexpansive multi-valued mappings and total asymptotically strict pseudo-contractive mapping. (English) Zbl 1302.47082
In this paper, the split feasibility problem for a family of quasi-nonexpansive multivalued mappings and a total asymptotically strict pseudocontractive mapping are studied in infinitely-dimensional Hilbert spaces. The main results presented in the paper improve and extend some recent results.
Reviewer: Zhang Xian (Xiamen)
MSC:
| 47H10 | Fixed-point theorems |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H04 | Set-valued operators |
Keywords:
split feasibility problem; convex feasibility problem; single-valued (multi-valued) quasi-nonexpansive mapping; demi-closedness; Opial’s condition; total asymptotically strict pseudocontractive mappingReferences:
| [1] | Yang, L.; Chang, S. S.; Cho, Y. J.; Kim, J. K., Multiple-set split feasibility problems for total asymptotically strict pseudocontractions mappings, Fixed Point Theory Appl., 2011, 77 (2011) · Zbl 1311.47101 |
| [2] | Goebel, K.; Kirk, W. A., A fixed point theorem for asymptotically nonexpansive mappings, Proc. Am. Math. Soc., 35, 171-174 (1972) · Zbl 0256.47045 |
| [4] | Byrne, C., Iterative oblique projection onto convex subsets and the split feasibility problem, Inverse Problem, 18, 441-453 (2002) · Zbl 0996.65048 |
| [5] | Censor, Y.; Bortfeld, T.; Martin, B.; Trofimov, A., A unified approach for inversion problem in intensity-modulated radiation therapy, Phys. Med. Biol., 51, 2353-2365 (2006) |
| [6] | Censor, Y.; Elfving, T.; Kopf, N.; Bortfeld, T., The multiple-sets split feasibility problem and its applications, Inverse Problem, 21, 2071-2084 (2005) · Zbl 1089.65046 |
| [7] | CensorX, Y.; Motova, A.; Segal, A., Pertured projections and subgradient projections for the multiple-setssplit feasibility problem, J. Math. Anal. Appl., 327, 1244-1256 (2007) · Zbl 1253.90211 |
| [8] | Xu, H. K., A variable Krasnosel’skii-Mann algorithm and the multiple-sets split feasibility problem, Inverse Problem, 22, 2021-2034 (2006) · Zbl 1126.47057 |
| [9] | Yang, Q., The relaxed CQ algorithm for solving the split feasibility problem, Inverse Problem, 20, 1261-1266 (2004) · Zbl 1066.65047 |
| [10] | Zhao, J.; Yang, Q., Several solution methods for the split feasibility problem, Inverse Problem, 21, 1791-1799 (2005) · Zbl 1080.65035 |
| [14] | Censor, Y.; Segal, A., The split common fixed point problem for directed operators, J. Convex Anal., 16, 587-600 (2009) · Zbl 1189.65111 |
| [15] | Masad, E.; Reich, S., A note on the multiple-set split feasibility problem in Hilbert spaces, J. Nonlinear Convex Anal., 8, 367-371 (2007) · Zbl 1171.90009 |
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