Abstract

In this paper, the most basic idea is to apply the viscosity approximation method to study the split feasibility problem (SFP), we will be in the infinite-dimensional Hilbert space to study the problem . We defined $x_{0}\in C$ as arbitrary and $x_{n+1}=(1-\alpha_{n})P_{C}(I-\lambda_{n}A^{*}(I-P_{Q})A)x_{n}+\alpha_{n}f(x_{n})$, for $n\geq0,$ where $\{\alpha_{n}\}\subset(0,1)$. Under the proper control conditions of some parameters, we show that the sequence $\{x_{n}\}$  converges strongly to a solution of SFP. The results in this paper extend and further improve the relevant conclusions in Deepho (Deepho, J. \& Kumam, P., 2015).

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