The Split Common Null Point Problem

By Charles L. Byrne, Yair Censor, Aviv Gibali, Simeon Reich. 2011

278 citations recorded by the source corpus.

We introduce and study the Split Common Null Point Problem (SCNPP) 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 nding a zero of a maximal monotone mapping in one space, the image of which

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/8dcae7c90d6735f4532b0e4229cdae1336316e91

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Citations in the corpus

The split common null point problem and the shrinking projection method in Banach spaces (2016, unknown): “[2] also considered the following problem: given set-valued mappings Ai : H1 → 2H1 , 1 ≤ i ≤ m, and B j : H2 → 2H2 , 1 ≤ j ≤ n, respectively, and bounded linear operators Tj : H1 → H2, 1 ≤ j ≤ n, the split common null point problem [2] is to find a point z ∈ H1 such that z ∈ ( m ⋂ i=1 A−1 i 0 ) ∩ ( ”
Iterative methods for solving the generalized split common null point problem in Hilbert spaces (2020, background): “4, where the coordinates of the centres a1, a2, a3 are randomly generated in [−1, 1], the radii R1,R2,R3 are randomly generated in the intervals [4, 8], [6, 12] and [8, 16], respectively, and the coordinates of the initial point x0 are randomly generated in [−2, 2].”
The shrinking projection method for a finite family of demimetric mappings with variational inequality problems in a Hilbert space (2018, background): “Thus, I − λA : C → H is nonexpansive; see [1, 11, 14] for more results of inversestrongly monotone mappings.”
Iterative approximation of a common solution of a split generalized equilibrium problem and a fixed point problem for nonexpansive semigroup (2013, background): “SEP (3)-(4) includes the split variational inequality problem, split zero problem, and split feasibility problem (see, for instance, [7-12]).”