Abstract
We introduce and analyze the viscosity approximation algorithm for solving the split common fixed point problem for the strictly pseudononspreading mappings in Hilbert spaces. Our results improve and develop previously discussed feasibility problems and related results.
Highlights
Throughout this paper, we always assume that H is a real Hilbert space with inner product ⟨⋅, ⋅⟩ and norm ‖ ⋅ ‖
We introduce and analyze the viscosity approximation algorithm for solving the split common fixed point problem for the strictly pseudononspreading mappings in Hilbert spaces
In 2012, Zhao and He [14] continue to consider the split common fixed point problem with quasi-nonexpansive operators and to use the following algorithm to obtain the strong convergence of the viscosity method for solving the split common fixed point problem
Summary
Throughout this paper, we always assume that H is a real Hilbert space with inner product ⟨⋅, ⋅⟩ and norm ‖ ⋅ ‖. Due to the fixed point formulation (2) of the SFP, Moudafi [11] applied the K-M algorithm to the operator PC (I − γA∗(I − PQ)A) to obtain a sequence given by xn+1 = (1 − αn) xn − αnPC (I − γA∗ (I − PQ) A) xn, (5). In 2012, Zhao and He [14] continue to consider the split common fixed point problem with quasi-nonexpansive operators and to use the following algorithm to obtain the strong convergence of the viscosity method for solving the split common fixed point problem. This paper establishes the strong convergence of the sequence given by (9) to the unique solution of solving the split common fixed point problem and the following variational inequality problem VIP(μB − σf, T): find x∗ ∈ Γ such that ⟨(μB − σf) x∗, V − x∗⟩ ≥ 0, (10)
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