In this paper, we introduce two algorithms for finding a common solution of the monotone inclusion problem and the fixed point problem for a relatively nonexpansive mapping in reflexive Banach spaces. The weak convergence results for both algorithms are established without the prior knowledge of the Lipschitz constant of the mapping. An application to the variational inequality problem is considered. Finally, some numerical experiments of the proposed algorithms including comparisons with other algorithms are provided.

中文翻译：

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自反Banach空间中单调包含问题和不动点问题的Mann型算法

在本文中，我们介绍了两种算法，用于找到自反Banach空间中相对非扩展映射的单调包含问题和不动点问题的通用解。在不事先了解映射的Lipschitz常数的情况下，建立了两种算法的弱收敛结果。考虑了变分不等式问题的一个应用。最后，提供了所提出算法的一些数值实验，包括与其他算法的比较。