In this work, we introduced an iterative algorithm for finding a common element of the set of common fixed points of a one-parameter nonexpansive semigroup, the set of solutions to a variational inclusion and the set of solutions to a generalized equilibrium problem in a real Hilbert space. Furthermore, we proved the convergence theorem of the proposed iterative algorithm under some mild conditions on algorithm parameters. Finally, we gave some numerical examples which support our main theorem at last part. The results presented in this paper generalize the well-known theorems.

中文翻译：

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为非膨胀半群、变分包含和广义均衡问题寻找公共不动点集合的公共元素的算法

在这项工作中，我们引入了一种迭代算法，用于寻找单参数非膨胀半群的公共不动点集的公共元素、变分包含的解集和实数中广义均衡问题的解集。希尔伯特空间。此外，我们在算法参数的一些温和条件下证明了所提出的迭代算法的收敛定理。最后，我们在最后部分给出了一些数值例子来支持我们的主要定理。本文中提出的结果概括了众所周知的定理。