This article considers and investigates a variational inequality problem and fixed-point problems in real Hilbert spaces endowed with graphs. A regularization method is proposed for solving a G-variational inequality problem and a common fixed-point problem of a finite family of G-nonexpansive mappings in the framework of Hilbert spaces endowed with graphs, which extends the work of Tiammee et al. (Fixed Point Theory Appl. 187, 2015) and Kangtunyakarn, A. (Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 112:437–448, 2018). Under certain conditions, a strong convergence theorem of the proposed method is proved. Finally, we provide numerical examples to support our main theorem. The numerical examples show that the speed of the proposed method is better than some recent existing methods in the literature.

中文翻译：

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求解赋予图的希尔伯特空间中G变分不等式问题和不动点问题的正则化方法

本文考虑并研究了图赋实希尔伯特空间中的变分不等式问题和不动点问题。提出了一种正则化方法来解决赋予图的 Hilbert 空间框架中的 G-变分不等式问题和有限族 G-非扩张映射的常见不动点问题，扩展了 Tiammee 等人的工作。(Fixed Point Theory Appl. 187, 2015) 和 Kangtunyakarn, A. (Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 112:437–448, 2018)。在一定条件下，证明了该方法的强收敛定理。最后，我们提供数值例子来支持我们的主要定理。数值例子表明，该方法的速度优于文献中一些最新的现有方法。