Abstract
In this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imposed on the sequences of parameters, some strong convergence theorems are proved, which also solve some variational inequalities that are closely related to optimization problems. The results here generalize and improve the main results of other authors.
Highlights
Since 1994, the split feasibility problem (SFP) [1,2,3] has received much attention, owing to its applications in many optimization problems, signal processing and medical image reconstruction with special progress in intensity-modulated radiation therapy [4,5,6]
In 2015, Tang et al [14] obtained a weak convergence theorem of the split common fixed point problem (SCFPP) for the asymptotically nonexpansive mapping S in Banach spaces of the following algorithm:
We present an iterative algorithm to approximate a solution of the SCFPP and show some strong convergence theorems under appropriate conditions, which solve some variational inequalities
Summary
Since 1994, the split feasibility problem (SFP) [1,2,3] has received much attention, owing to its applications in many optimization problems, signal processing and medical image reconstruction with special progress in intensity-modulated radiation therapy [4,5,6]. In 2015, Tang et al [14] obtained a weak convergence theorem of the SCFPP for the asymptotically nonexpansive mapping S in Banach spaces of the following algorithm:
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