In this paper, we construct a forward–backward splitting algorithm for approximating a zero of the sum of an \(\alpha \)-inverse strongly monotone operator and a maximal monotone operator. The strong convergence theorem is then proved under mild conditions. Then, we add a nonexpansive mapping in the algorithm and prove that the generated sequence converges strongly to a common element of a fixed points set of a nonexpansive mapping and zero points set of the sum of monotone operators. We apply our main result both to equilibrium problems and convex programming.

中文翻译：

---

定点问题和单调算子和的零的正向拆分算法

在本文中，我们构造了一个前向后拆分算法，用于近似逼近\（\ alpha \）逆强单调算子和最大单调算子的和。然后在温和条件下证明了强收敛定理。然后，我们在算法中添加了非扩展映射，并证明了生成的序列强烈收敛到非扩展映射的不动点集和单调算子和的零点集的公共元素。我们将主要结果应用于均衡问题和凸规划。