article published yes Olaniyi S. Iyiola author Cyril D. Enyi author Yekini Shehu author 3FC7CB58-F248-11E8-B48F-1D18A9856A870000-0001-9224-7139 VlKo department Discrete Optimization in Computer Vision: Theory and Practice project In this paper, we consider reflected three-operator splitting methods for monotone inclusion problems in real Hilbert spaces. To do this, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the reflected Krasnosel'skiĭ-Mann iteration for finding a fixed point of nonexpansive mapping in real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. We then apply our results to three-operator splitting for the monotone inclusion problem and consequently obtain the corresponding convergence analysis. Furthermore, we derive reflected primal-dual algorithms for highly structured monotone inclusion problems. Some numerical implementations are drawn from splitting methods to support the theoretical analysis. Taylor & Francis2022 eng 1055-6788 1029-4937 00065050760000110.1080/10556788.2021.1924715 3741527-1565 O. S. Iyiola, C. D. Enyi, and Y. Shehu, “Reflected three-operator splitting method for monotone inclusion problem,” <i>Optimization Methods and Software</i>, vol. 37, no. 4. Taylor &#38; Francis, pp. 1527–1565, 2022. Iyiola OS, Enyi CD, Shehu Y. Reflected three-operator splitting method for monotone inclusion problem. <i>Optimization Methods and Software</i>. 2022;37(4):1527-1565. doi:<a href="https://doi.org/10.1080/10556788.2021.1924715">10.1080/10556788.2021.1924715</a> Iyiola, O. S., Enyi, C. D., &#38; Shehu, Y. (2022). Reflected three-operator splitting method for monotone inclusion problem. <i>Optimization Methods and Software</i>. Taylor &#38; Francis. <a href="https://doi.org/10.1080/10556788.2021.1924715">https://doi.org/10.1080/10556788.2021.1924715</a> Iyiola, Olaniyi S., Cyril D. Enyi, and Yekini Shehu. “Reflected Three-Operator Splitting Method for Monotone Inclusion Problem.” <i>Optimization Methods and Software</i>. Taylor &#38; Francis, 2022. <a href="https://doi.org/10.1080/10556788.2021.1924715">https://doi.org/10.1080/10556788.2021.1924715</a>. Iyiola, Olaniyi S., et al. “Reflected Three-Operator Splitting Method for Monotone Inclusion Problem.” <i>Optimization Methods and Software</i>, vol. 37, no. 4, Taylor &#38; Francis, 2022, pp. 1527–65, doi:<a href="https://doi.org/10.1080/10556788.2021.1924715">10.1080/10556788.2021.1924715</a>. Iyiola OS, Enyi CD, Shehu Y. 2022. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. 37(4), 1527–1565. O.S. Iyiola, C.D. Enyi, Y. Shehu, Optimization Methods and Software 37 (2022) 1527–1565. 94692021-06-06T22:01:30Z2026-07-07T05:33:15Z