We propose a Halpern-type forward-backward splitting with inertial extrapolation step for finding a zero of the sum of accretive operators in Banach spaces. Strong convergence of the sequence of iterates generated by the method proposed is obtained under mild assumptions. We give some numerical results in compressed sensing to validate the theoretical analysis results. Our result is one of the lew available inertial-type methods for zeros of the sum of accretive operators in Banach spaces.

中文翻译：

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Banach空间惯性前向后向分裂方法在压缩感知中的应用

我们提出了一种带有惯性外推步骤的 Halpern 型前向后向分裂，用于在 Banach 空间中找到增殖算子之和的零。由所提出的方法生成的迭代序列的强收敛是在温和的假设下获得的。我们在压缩感知中给出了一些数值结果来验证理论分析结果。我们的结果是用于 Banach 空间中增生算子和的零点的 lew 可用惯性类型方法之一。