Guan Jin-Lin, Ceng Lu-Chuan, Hu Bing
1Department of Mathematics, Shanghai Normal University, Shanghai, China.
2LAMPS and Department of Mathematics and Statistics, York University, Toronto, Canada.
J Inequal Appl. 2018;2018(1):311. doi: 10.1186/s13660-018-1905-6. Epub 2018 Nov 15.
In this paper, inspired by Jitsupa et al. (J. Comput. Appl. Math. 318:293-306, 2017), we propose a general iterative scheme for finding a solution of a split monotone variational inclusion with the constraints of a variational inequality and a fixed point problem of a finite family of strict pseudo-contractions in real Hilbert spaces. Under very mild conditions, we prove a strong convergence theorem for this iterative scheme. Our result improves and extends the corresponding ones announced by some others in the earlier and recent literature.
在本文中，受吉苏帕等人（《计算与应用数学杂志》318:293 - 306，2017）的启发，我们提出了一种通用的迭代方案，用于在实希尔伯特空间中找到一个分裂单调变分包含问题的解，该问题带有一个变分不等式的约束以及一族有限严格伪压缩映射的不动点问题。在非常温和的条件下，我们证明了该迭代方案的一个强收敛定理。我们的结果改进并扩展了早期和近期文献中其他一些人所宣布的相应结果。
