Abstract
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 language | English |
|---|---|
| Pages (from-to) | 759-775 |
| Number of pages | 17 |
| Journal | Journal of Nonlinear and Convex Analysis |
| Volume | 13 |
| Issue number | 4 |
| State | Published - Oct 2012 |
Keywords
- 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