Quan, Jing; Chang, Shih-sen; Zhang, Xiang Multiple-set split feasibility problems for \(\kappa\)-strictly pseudononspreading mapping in Hilbert spaces. (English) Zbl 1291.47059 Abstr. Appl. Anal. 2013, Article ID 342545, 5 p. (2013). Summary: The purpose of this paper is to prove some weak and strong convergence theorems for solving the multiple-set split feasibility problems for \(\kappa\)-strictly pseudononspreading mapping in infinite-dimensional Hilbert spaces by using the proposed iterative method. The main results presented in this paper extend and improve corresponding results, and of many other authors. Cited in 6 Documents MSC: 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. PDF BibTeX XML Cite \textit{J. Quan} et al., Abstr. Appl. Anal. 2013, Article ID 342545, 5 p. (2013; Zbl 1291.47059) Full Text: DOI References: [1] 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 [2] Byrne, C., Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems, 18, 2, 441-453 (2002) · Zbl 0996.65048 [3] 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, 10, 2353-2365 (2006) [4] Censor, Y.; Elfving, T.; Kopf, N.; Bortfeld, T., The multiple-sets split feasibility problem and its applications for inverse problems, Inverse Problems, 21, 6, 2071-2084 (2005) · Zbl 1089.65046 [5] Censor, Y.; Motova, A.; Segal, A., Perturbed projections and subgradient projections for the multiple-sets split feasibility problem, Journal of Mathematical Analysis and Applications, 327, 2, 1244-1256 (2007) · Zbl 1253.90211 [6] Xu, H.-K., A variable Krasnoselskii-Mann algorithm and the multiple-set split feasibility problem, Inverse Problems, 22, 6, 2021-2034 (2006) · Zbl 1126.47057 [7] Kohsaka, F.; Takahashi, W., Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces, Archiv der Mathematik, 91, 2, 166-177 (2008) · Zbl 1149.47045 [8] Kohsaka, F.; Takahashi, W., Existence and approximation of fixed points of firmly nonexpansive-type mappings in Banach spaces, SIAM Journal on Optimization, 19, 2, 824-835 (2008) · Zbl 1168.47047 [9] Iemoto, S.; Takahashi, W., Approximating common fixed points of nonexpansive mappings and nonspreading mappings in a Hilbert space, Nonlinear Analysis: Theory, Methods & Applications, 71, 12, e2082-e2089 (2009) · Zbl 1239.47054 [10] Browder, F. E.; Petryshyn, W. V., Construction of fixed points of nonlinear mappings in Hilbert space, Journal of Mathematical Analysis and Applications, 20, 197-228 (1967) · Zbl 0153.45701 [11] Osilike, M. O.; Isiogugu, F. O., Weak and strong convergence theorems for nonspreading-type mappings in Hilbert spaces, Nonlinear Analysis: Theory, Methods & Applications, 74, 5, 1814-1822 (2011) · Zbl 1281.47050 [12] Kurokawa, Y.; Takahashi, W., Weak and strong convergence theorems for nonspreading mappings in Hilbert spaces, Nonlinear Analysis: Theory, Methods & Applications, 73, 6, 1562-1568 (2010) · Zbl 1229.47117 [13] Deepho, J.; Kumam, P., A modified Halpern’s iterative scheme for solving split feasibility problems, Abstract and Applied Analysis, 2012 (2012) · Zbl 1253.65093 [14] Deepho, J.; Kumam, P., Split feasibility and fixed-point problems for asymptotically quasi-nonexpansive mappings, Journal of Inequalities and Applications, 2013, 322 (2013) · Zbl 06269440 [15] Sunthrayuth, P.; Cho, Y. J.; Kumam, P., General iterative algorithms approach to variational inequalities and minimum-norm fixed point for minimization and split, OPSEARCH (2013) · Zbl 1332.90342 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.