In this paper, we propose a generalized viscosity explicit method for finding zeros of the sum of two accretive operators in the framework of Banach spaces. The strong convergence theorem of such method is proved under some suitable assumption on the parameters. As applications, we apply our main result to the variational inequality problem, the convex minimization problem and the split feasibility problem. The numerical experiments to illustrate the behaviour of the proposed method including compare it with other methods are also presented.

中文翻译：

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Banach空间中求解变分包含问题的广义粘度显式规则

在本文中，我们提出了一种广义粘度显式方法，用于在 Banach 空间的框架内寻找两个增值算子之和的零点。该方法的强收敛定理在参数的一些适当假设下得到证明。作为应用，我们将我们的主要结果应用于变分不等式问题、凸最小化问题和分裂可行性问题。还介绍了用于说明所提出方法的行为的数值实验，包括将其与其他方法进行比较。