The split common null point problem

Charles Byrne, Yair Censor, Aviv Gibali, Simeon Reich

Research output: Contribution to journalArticlepeer-review


We introduce and study the Split Common Null Point Problem (SC-NPP) for set-valued maximal monotone mappings in Hilbert spaces. This problem generalizes our Split Variational Inequality Problem (SVIP) [Y. Censor, A. Gibali and S. Reich, Algorithms for the split variational inequality problem, Numerical Algorithms 59 (2012), 301-323]. The SCNPP with only two set-valued mappings entails finding a zero of a maximal monotone mapping in one space, the image of which under a given bounded linear transformation is a zero of another maximal monotone mapping. We present four iterative algorithms that solve such problems in Hilbert spaces, and establish weak convergence for one and strong convergence for the other three.

Original languageEnglish
Pages (from-to)759-775
Number of pages17
JournalJournal of Nonlinear and Convex Analysis
Issue number4
StatePublished - Oct 2012


  • Averaged operator
  • Cutter operator
  • Firmly nonexpansive operator
  • Hilbert space
  • Iterative algorithm
  • Maximal monotone mapping
  • Split common null point problem
  • Split convex feasibility problem
  • Split inverse problem
  • Split variational inequality problem

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Control and Optimization
  • Applied Mathematics


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