Byrne, Charles; Censor, Yair; Gibali, Aviv; Reich, Simeon The split common null point problem. (English) Zbl 1262.47073 J. Nonlinear Convex Anal. 13, No. 4, 759-775 (2012). In this paper, the authors study the Split Null Point Problem for set-valued mappings in Hilbert spaces. More precisely, if \(H_1, H_2\) are two Hilbert spaces, \(B_i:H_1\to 2^{H_1}\) for \(1\leq i\leq p\), respectively \(F_j:H_2\to 2^{H_2}\) for \(1\leq j\leq r\), are given set-valued operators and \(A_j:H_1\to H_2\) for \(1\leq j\leq r\) are bounded linear operators, the problem is to find \(x^*\in H_1\) such that \(0\in \bigcap_{i=1}^pB_i(x^*)\) and such that the points \(y_j^*=A_j(x^*)\) solve \(0\in \bigcap_{j=1}^{r}F_j(y_j^*)\). Iterative algorithms are proposed and weak/strong convergence theorems are given. Reviewer: Adrian Petruşel (Cluj-Napoca) Cited in 5 ReviewsCited in 234 Documents MSC: 47H04 Set-valued operators 49J40 Variational inequalities 90C25 Convex programming Keywords:averaged operator; cutter operator; Hilbert space; firmly nonexpansive operator; iterative algorithm; maximal monotone mapping; split common null point problem; split convex feasibility problem; split inverse problem; split variational inequality problem PDFBibTeX XMLCite \textit{C. Byrne} et al., J. Nonlinear Convex Anal. 13, No. 4, 759--775 (2012; Zbl 1262.47073) Full Text: arXiv Link