Abstract
The split common fixed point problem has been investigated recently, which is a generalization of the split feasibility problem and of the convex feasibility problem. We construct a cyclic algorithm to approximate a solution of the split common fixed point problem for the demicontractive mappings in a Hilbert space. Our results improve and extend previously discussed related problems and algorithms.
Highlights
Let H be a real Hilbert space with inner product ·,· and norm ·, respectively.Recall that the convex feasibility problem (CFP) is formulated as follows: If n i=1 Ci = ∅, nFind a point x∗ ∈ Ci, (1.1)i=1 where n ≥ 1 is an integer, and each Ci is a nonempty closed convex subset of H
The problems (1.2) and (1.4) are all special cases of the so-called split common fixed point problem (SCFP) which is formulated as follow: p r
Censor and Segal [7] constructed the following algorithms to solve the two sets of (SCFP) for directed operators
Summary
The problems (1.2) and (1.4) are all special cases of the so-called split common fixed point problem (SCFP) which is formulated as follow: p r Censor and Segal [7] constructed the following algorithms to solve the two sets of (SCFP) for directed operators (the definition is given by Definition 2). Let x0 ∈ H1 be arbitrary, the sequence {xn} defined by: xn+1 = U xn − γA∗(I − T )Axn , n ≥ 0, where γ
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