Iterative methods for solving split feasibility problems and fixed point problems in Banach spaces. (English) Zbl 1498.47130
Summary: In this paper, we consider a class of split feasibility problems in Banach space. By using shrinking projective method and the modified proximal point algorithm, we propose an iterative algorithm. Under suitable conditions some strong convergence theorems are proved. Our results extend a recent result of Takahashi-Xu-Yao [W. Takahashi et al., Set-Valued Var. Anal. 23, No. 2, 205–221 (2015; Zbl 1326.47099)] from Hilbert spaces to Banach spaces. Moreover, the method of proof is also different.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 49J40 | Variational inequalities |
| 90C25 | Convex programming |
| 90C48 | Programming in abstract spaces |
Keywords:
split feasibility problem; maximal monotone operators; shrinking projective method; modified proximal point algorithm; strong convergenceCitations:
Zbl 1326.47099References:
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