Abstract
The purpose of this paper is to prove some weak and strong convergence theorems for solving the multiple-set split feasibility problems forκ-strictly pseudononspreading mapping in infinite-dimensional Hilbert spaces by using the proposed iterative method. The main results presented in this paper extend and improve the corresponding results of Xu et al. (2006), of Osilike et al. (2011), and of many other authors.
Highlights
Introduction and PreliminariesCensor and Elfving first introduced the split feasibility problem (SFP) [1] in finite dimensional spaces for modeling inverse problems
The so-called multiple-set split feasibility problem (MSSFP) is to find x∗ ∈ C such that Ax∗ ∈ Q, where A : H1 → H2 is a bounded linear operator, Si and Ti, i = 1, 2, . . . , N are the families of mappings, Si : H1 → H1 and Ti : H2 → H2, C := ⋂Ni=1 F(Si), and Q := ⋂Ni=1 F(Ti), where F(Si) = {x ∈ H1 : Six = x} and F(Ti) = {y ∈ H2 : Tiy = y} denote the sets of fixed points of Si and Ti, respectively
We use Γ to denote the set of solutions of the MSSFP; that is, Γ = {x ∈ C : Ax ∈ Q}
Summary
Introduction and PreliminariesCensor and Elfving first introduced the split feasibility problem (SFP) [1] in finite dimensional spaces for modeling inverse problems. We always assume that H1, H2 are two real Hilbert spaces and denote by “ → ” and “⇀” the strong and weak convergence, respectively. Let K be a nonempty closed convex subset of a Hilbert space H.
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